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Numbers k such that prepending 3 to the k-th triangular number produces a prime.
1

%I #6 Jul 14 2021 01:55:32

%S 22,46,61,82,106,118,181,286,301,373,406,433,481,493,526,562,577,661,

%T 733,802,817,886,946,961,1033,1162,1177,1246,1258,1261,1297,1342,1426,

%U 1513,1546,1558,1573,1618,1741,1813,1822,1846,1873,1882,1918,1921,1957

%N Numbers k such that prepending 3 to the k-th triangular number produces a prime.

%C Or, concatenated T(2) and T(k) are prime. Or, concatenated A000217(2) and A000217(k) are prime.

%e T(2)=253, 3253 is prime, so 22 is a term;

%e T(46)=1081, 31081 is prime, so 46 is a term;

%e T(61)=1891, 31891 is prime, so 61 is a term.

%Y Cf. A000217, A158844, A158845, A158750.

%K base,nonn

%O 1,1

%A _Zak Seidov_, Mar 28 2009