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 A125251 a(n)=sqrt(A051779(n+2)-1)/30. 4
 5, 6, 8, 9, 14, 19, 43, 44, 77, 85, 91, 112, 113, 142, 155, 195, 196, 212, 226, 300, 308, 321, 351, 363, 399, 456, 461, 467, 485, 541, 555, 602, 604, 618, 638, 646, 720, 728, 779, 789, 891, 896, 923, 980, 1009, 1099, 1105, 1150, 1176, 1234, 1253, 1287, 1392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Consider twin primes p, q = p + 2 such that pq + 2 is prime. It would seem that there are infinitely many such p. Except for p = 3 and p = 5 all such p appear to be of the form 30k - 1 and the values of k give the current sequence. - James R. Buddenhagen, Jan 09 2007 This is true. Prime numbers (other than 2,3,5) are 30k + 1,7,11,13,17,19,23,29. p+2 is then prime only for p = 30k + 11,17,29; then p(p+2)+2 is 30k + 25,25,1 respectively, so the last case mod 30 is the only one possible. - Gareth McCaughan (gareth.mccaughan(AT)pobox.com), Jan 09 2007 This is the sequence of positive integers k such that p = 30*k - 1, q = 30*k + 1 and p*q + 2 are all prime. - James R. Buddenhagen, Jan 09 2007 LINKS Zak Seidov, Table of n, a(n) for n=1..2000 EXAMPLE a(1)=5 because A051779(3)=22501 and sqrt(22501-1)/30=5, a(2)=6 because A051779(4)=32401 and sqrt(32401-1)/30=6. PROG (PARI) isok(n) = isprime(p = 30*n+1) && isprime(q = 30*n-1) && isprime(p*q+2); \\ Michel Marcus, Oct 11 2013 CROSSREFS Cf. A051779. Sequence in context: A187843 A155146 A308708 * A271728 A247047 A218866 Adjacent sequences: A125248 A125249 A125250 * A125252 A125253 A125254 KEYWORD nonn AUTHOR Zak Seidov, Nov 26 2006 STATUS approved

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Last modified November 28 22:51 EST 2022. Contains 358421 sequences. (Running on oeis4.)