Sorry, Dan, to have proposed puzzles #2 and #3 on your puzzle #1... ...without any connection, except of course "1,2,3,5,18". Because you give your solution, I am now forced to give my solutions, hoping that they are correct. First solutions of puzzle #2: 1, 2, 3, 5, 18, 9131330, ... First solutions of puzzle #3: 1, 2, 3, 5, 18, 16954445, ... Their 6th terms are surprisingly big, it was my goal. But smaller than the term proposed by Marc LeBrun on puzzle #1 ;-) Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : samedi 9 septembre 2006 14:43 À : 'math-fun'; 'Daniel Asimov' Objet : RE: [math-fun] 1,2,3,5,18 puzzle Integers n producing 8 prime numbers: (2n+1, 4n-1, 6n-1, 6n+1, 10n-7, 14n-11, 18n-7, 30n+7) n = 1, 2, 3, 5, 18 are the smallest solutions. New puzzle #2: what is the next solution? New puzzle #3: if you replace 6n-1 by 48n-43, what is the next solution? Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : vendredi 8 septembre 2006 10:45 À : 'Daniel Asimov'; 'math-fun' Objet : RE: [math-fun] 1,2,3,5,18 puzzle An answer, but not your answer, and not a conjecture ;-) 1, 2, 3, 5, 18 are the only integers n < 23 where: (2n+1, 6n+1, 6n-1) are prime numbers Christian. (next are 23, 30, 33, 95,... ) -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Daniel Asimov Envoyé : vendredi 8 septembre 2006 01:58 À : math-fun Objet : Re: [math-fun] 1,2,3,5,18 puzzle << Puzzle: What do the positive integers 1, 2, 3, 5, 18 have in common with each other, but with no other positive integer (conjecturally)
To clarify: There is no "catch", and the answer is purely mathematical. --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun