[math-fun] a(n) = PrimePi(a(n+1))
Hello Math-Fun, as I get this from SeqFans (which I don't understand) I beg for mercy re-sending my post here. Best, É. --- Certains des destinataires ou tous les destinataires n'ont pas reçu votre message. Objet : a(n) = PrimePi(a(n+1)) Date : 17/09/2008 15:33 Impossible de contacter le(s) destinataire(s) suivant(s) : seqfan@ext.jussieu.fr le 17/09/2008 15:32 L'organisation à laquelle le message a été envoyé a indiqué qu'elle ne contenait pas ce compte de messagerie. Vérifiez l'adresse de messagerie du destinataire ou bien contactez le destinataire directement pour lui demander son adresse exacte. < shiva.jussieu.fr #5.1.1 smtp; 550 5.1.1 <seqfan@ext.jussieu.fr>... User unknown> --- Hello SeqFans, Could someone please compute a few more (not too big) terms? Best, É. http://www.research.att.com/~njas/sequences/A000720 0,1,2,3,5,11,31,127,... a(n) is the smallest integer equal to PrimePi(a(n+1)) [this is a very, very bad mixture of pidgenglish and maths -- sorry. How could the seq be properly defined?] (done by hand using this table: http://www.research.att.com/~njas/sequences/b000720.txt ) Method (see table below): - start with the first 0 on the right 0 - this 0 comes from 1, on the left - look for the first 1 on the right 1 - this 1 comes from 2, on the left - look for the first 2 on the right 2 - this 2 comes from 3, on the left - look for the first 3 on the right 3 - this 3 comes from 5, on the left - look for the first 5 on the right 5 - this 5 comes from 11, on the left - look for the first 11 on the right 11 - this 11 comes from 31, on the left - look for the first 31 on the right 31 - this 31 comes from 127, on the left - look for the first 127 on the right 127 ... 1 0 <-- 2 1 <-- 3 2 <-- 4 2 5 3 <-- 6 3 7 4 8 4 9 4 10 4 11 5 <-- 12 5 13 6 14 6 15 6 16 6 17 7 18 7 19 8 20 8 21 8 22 8 23 9 24 9 25 9 26 9 27 9 28 9 29 10 30 10 31 11 <-- 32 11 33 11 34 11 35 11 36 11 37 12 38 12 39 12 40 12 41 13 42 13 43 14 44 14 45 14 46 14 47 15 48 15 49 15 50 15 51 15 52 15 53 16 54 16 55 16 56 16 57 16 58 16 59 17 60 17 61 18 62 18 63 18 64 18 65 18 66 18 67 19 68 19 69 19 70 19 71 20 72 20 73 21 74 21 75 21 76 21 77 21 78 21 79 22 80 22 81 22 82 22 83 23 84 23 85 23 86 23 87 23 88 23 89 24 90 24 91 24 92 24 93 24 94 24 95 24 96 24 97 25 98 25 99 25 100 25 101 26 102 26 103 27 104 27 105 27 106 27 107 28 108 28 109 29 110 29 111 29 112 29 113 30 114 30 115 30 116 30 117 30 118 30 119 30 120 30 121 30 122 30 123 30 124 30 125 30 126 30 127 31 <-- 128 31 129 31 130 31 131 32 ... Best, É.
Isn't this just a(n) = the a(n-1)'th prime? Mma: NestList[Prime, 1, 15] {1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101, 88362852307, 2428095424619} In fact, it's http://www.research.att.com/~njas/sequences/A007097 --Michael On Wed, Sep 17, 2008 at 9:42 AM, Eric Angelini <Eric.Angelini@kntv.be>wrote:
Hello Math-Fun, as I get this from SeqFans (which I don't understand) I beg for mercy re-sending my post here. Best, É.
---
Certains des destinataires ou tous les destinataires n'ont pas reçu votre message. Objet : a(n) = PrimePi(a(n+1)) Date : 17/09/2008 15:33 Impossible de contacter le(s) destinataire(s) suivant(s) : seqfan@ext.jussieu.fr le 17/09/2008 15:32 L'organisation à laquelle le message a été envoyé a indiqué qu'elle ne contenait pas ce compte de messagerie. Vérifiez l'adresse de messagerie du destinataire ou bien contactez le destinataire directement pour lui demander son adresse exacte. < shiva.jussieu.fr #5.1.1 smtp; 550 5.1.1 <seqfan@ext.jussieu.fr>... User unknown>
---
Hello SeqFans, Could someone please compute a few more (not too big) terms? Best, É. http://www.research.att.com/~njas/sequences/A000720<http://www.research.att.com/%7Enjas/sequences/A000720>
0,1,2,3,5,11,31,127,...
a(n) is the smallest integer equal to PrimePi(a(n+1)) [this is a very, very bad mixture of pidgenglish and maths -- sorry. How could the seq be properly defined?]
(done by hand using this table: http://www.research.att.com/~njas/sequences/b000720.txt<http://www.research.att.com/%7Enjas/sequences/b000720.txt>)
Method (see table below): - start with the first 0 on the right 0 - this 0 comes from 1, on the left - look for the first 1 on the right 1 - this 1 comes from 2, on the left - look for the first 2 on the right 2 - this 2 comes from 3, on the left - look for the first 3 on the right 3 - this 3 comes from 5, on the left - look for the first 5 on the right 5 - this 5 comes from 11, on the left - look for the first 11 on the right 11 - this 11 comes from 31, on the left - look for the first 31 on the right 31 - this 31 comes from 127, on the left - look for the first 127 on the right 127 ...
1 0 <-- 2 1 <-- 3 2 <-- 4 2 5 3 <-- 6 3 7 4 8 4 9 4 10 4 11 5 <-- 12 5 13 6 14 6 15 6 16 6 17 7 18 7 19 8 20 8 21 8 22 8 23 9 24 9 25 9 26 9 27 9 28 9 29 10 30 10 31 11 <-- 32 11 33 11 34 11 35 11 36 11 37 12 38 12 39 12 40 12 41 13 42 13 43 14 44 14 45 14 46 14 47 15 48 15 49 15 50 15 51 15 52 15 53 16 54 16 55 16 56 16 57 16 58 16 59 17 60 17 61 18 62 18 63 18 64 18 65 18 66 18 67 19 68 19 69 19 70 19 71 20 72 20 73 21 74 21 75 21 76 21 77 21 78 21 79 22 80 22 81 22 82 22 83 23 84 23 85 23 86 23 87 23 88 23 89 24 90 24 91 24 92 24 93 24 94 24 95 24 96 24 97 25 98 25 99 25 100 25 101 26 102 26 103 27 104 27 105 27 106 27 107 28 108 28 109 29 110 29 111 29 112 29 113 30 114 30 115 30 116 30 117 30 118 30 119 30 120 30 121 30 122 30 123 30 124 30 125 30 126 30 127 31 <-- 128 31 129 31 130 31 131 32 ...
Best, É.
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participants (2)
-
Eric Angelini -
Michael Kleber