[math-fun] Sum of peculiar primes
Hello Math-Fun, We look for integers that are the sum of certain primes: 32 = 3 + 29 117 = 19 + 19 + 79 119 = 11 + 11 + 97 127 = 19 + 29 + 79 139 = 11 + 31 + 97 ... If we keep the first digit of the summed terms and concatenate them, we form the sum again, in those equations. Any others? (yes, there is sometimes a trick: the last equation produces 169 = 11 + 61 + 97 and 179 = 11 + 71 + 97, for instance). Best, É.
Should the sum be a prime too (like 127 or 139) we could call those integers « acronym primes » or « acronymic primes » (if this is not old hat). Best, É.
Le 24 déc. 2020 à 01:41, Éric Angelini <eric.angelini@skynet.be> a écrit :
Hello Math-Fun, We look for integers that are the sum of certain primes: 32 = 3 + 29 117 = 19 + 19 + 79 119 = 11 + 11 + 97 127 = 19 + 29 + 79 139 = 11 + 31 + 97 ... If we keep the first digit of the summed terms and concatenate them, we form the sum again, in those equations. Any others? (yes, there is sometimes a trick: the last equation produces 169 = 11 + 61 + 97 and 179 = 11 + 71 + 97, for instance). Best, É.
2, 3, 5, and 7 are trivial solutions. 21 = 2 + 19. Numbers expressible in this form might make an interesting sequence. On Wed, Dec 23, 2020 at 7:54 PM Éric Angelini <eric.angelini@skynet.be> wrote:
Should the sum be a prime too (like 127 or 139) we could call those integers « acronym primes » or « acronymic primes » (if this is not old hat). Best, É.
Le 24 déc. 2020 à 01:41, Éric Angelini <eric.angelini@skynet.be> a écrit :
Hello Math-Fun, We look for integers that are the sum of certain primes: 32 = 3 + 29 117 = 19 + 19 + 79 119 = 11 + 11 + 97 127 = 19 + 29 + 79 139 = 11 + 31 + 97 ... If we keep the first digit of the summed terms and concatenate them, we form the sum again, in those equations. Any others? (yes, there is sometimes a trick: the last equation produces 169 = 11 + 61 + 97 and 179 = 11 + 71 + 97, for instance). Best, É.
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participants (2)
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Allan Wechsler -
Éric Angelini