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%I #10 Jul 14 2021 01:55:36
%S 13,37,73,118,166,217,313,433,457,493,538,541,553,601,613,637,706,826,
%T 853,898,958,1042,1057,1138,1222,1357,1441,1513,1666,1681,1777,1858,
%U 1966,1993,2173,2281,2341,2422,2446,2518,2626,2638,2653,2686,2701,2737
%N Numbers k such that prepending 6 to the k-th triangular number produces a prime.
%C Or, concatenated T(3) and T(k) are prime. Or, concatenated A000217(3) and A000217(k) are prime.
%H Harvey P. Dale, <a href="/A158864/b158864.txt">Table of n, a(n) for n = 1..1000</a>
%e T(13)=91, 691 is prime, so 13 is a term;
%e T(37)=703, 6703 is prime, so 37 is a term;
%e T(73)=2701, 62701 is prime, so 73 is a term.
%t Rest[Flatten[Position[Accumulate[Range[3000]],_?(PrimeQ[ 6*10^IntegerLength[ #]+#]&)]]] (* _Harvey P. Dale_, Jul 27 2015 *)
%Y Cf. A000217, A158844, A158862, A158845, A158750.
%K base,nonn
%O 1,1
%A _Zak Seidov_, Mar 28 2009
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