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%I #11 Jul 14 2021 01:55:26
%S 1,2,13,17,18,21,38,41,62,66,77,97,98,106,117,118,133,146,153,157,161,
%T 178,181,197,198,202,206,217,222,226,233,237,242,257,261,266,286,297,
%U 301,302,318,321,322,338,346,362,373,377,393,402,413,421,422,453,461,462
%N Numbers k such that prepending 1 to the k-th triangular number produces a prime.
%C Or, concatenating T(1) and T(k) produces a prime, or, concatenating A000217(1) and A000217(k) produces a prime.
%H Harvey P. Dale, <a href="/A158845/b158845.txt">Table of n, a(n) for n = 1..1000</a>
%e T(2)=3, 13 is prime, so 2 is a term;
%e T(13)=91, 191 is prime, so 13 is a term;
%e T(17)=153, 1153 is prime, so 17 is a term.
%t Rest[Select[Range[600],PrimeQ[FromDigits[Join[{1},IntegerDigits[(# (#+1))/2]]]]&]] (* _Harvey P. Dale_, Apr 15 2009 *)
%t trprQ[n_]:=Module[{tr=(n(n+1))/2},PrimeQ[10^IntegerLength[tr]+tr]]; Select[ Range[ 500],trprQ] (* _Harvey P. Dale_, Aug 04 2019 *)
%Y Cf. A000217, A158844, A158750.
%K nonn,base
%O 1,2
%A _Zak Seidov_, Mar 28 2009
%E First term (1) prepended by _Harvey P. Dale_, Aug 04 2019
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