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%I #9 Jul 14 2021 01:55:20
%S 20,31,35,39,44,99,135,139,155,164,200,211,271,275,284,340,359,360,
%T 404,416,424,444,484,496,511,564,596,611,640,676,724,800,836,859,860,
%U 871,876,884,919,940,944,951,971,976,995,1000,1004,1064,1116,1131,1144,1159
%N Numbers k such that the concatenation of triangular numbers T(k), T(k+1) and T(k+2) is prime.
%e T(20) = 210, T(21) = 231, T(22) = 253, and 210231253 is prime, so 20 is a term;
%e T(31) = 496, T(32) = 528, T(33) = 561, and 496528561 is prime, so 31 is a term.
%t p3cQ[n_]:=Module[{c1=(n(n+1))/2,c2=((n+1)(n+2))/2,c3=((n+2)(n+3))/2}, PrimeQ[FromDigits[Flatten[IntegerDigits/@{c1,c2,c3}]]]]; Select[Range[ 1250], p3cQ] (* _Harvey P. Dale_, Sep 13 2011 *)
%Y Cf. A158750, A000217.
%K nonn,base
%O 1,1
%A _Zak Seidov_, Mar 28 2009