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%I #6 Mar 30 2012 17:40:18
%S 3,3,1,19,1,1,1,1,1,1,9,11,11,17,3,1,1,3,11,17,21,19,1,7,37,7,23,37,7,
%T 1,7,7,7,11,7,33,29,31,1,13,11,17,7,11,11,9,9,1,7,7,1,13,11,19,67,1,
%U 13,21,49,13,13,1,1,23,1,1,29,1,29,7
%N The smallest integer k>0 such that the double-concatenation prime(n) // prime(n+1) // k is a prime number.
%C Leading zeros in k are not allowed.
%C All entries k are odd with final digit 1, 3, 7 or 9.
%C Dirichlet's prime number theorem for arithmetic progressions says that the sequence is infinite.
%C Conjecture: 1 appears infinitely often.
%e n=1: 2//3//1 = 231 = 3 * 7 * 11 is not prime, so k<>1. 233 = prime(51), therefore 3 is the first entry.
%e n=2: 3//5//1 = 351 = 3^3 * 13 is not prime, so k <> 1, but 353 = prime(71), therefore 3 is the second entry.
%e n=30: 113//127//1 = 1131271 = prime(87976), so the 30th entry is 1.
%p read("transforms") ;
%p A174031 := proc(n) for e from 1 do if isprime(digcatL([ithprime(n),ithprime(n+1),e])) then return e ; end if; end do: end proc:
%Y Cf. A030461, A030459, A030469, A171154
%K base,nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 06 2010
%E Entries checked; replaced variables by OEIS standard names - _R. J. Mathar_, Nov 17 2010
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