A158845 Numbers k such that prepending 1 to the k-th triangular number produces a prime.

1, 2, 13, 17, 18, 21, 38, 41, 62, 66, 77, 97, 98, 106, 117, 118, 133, 146, 153, 157, 161, 178, 181, 197, 198, 202, 206, 217, 222, 226, 233, 237, 242, 257, 261, 266, 286, 297, 301, 302, 318, 321, 322, 338, 346, 362, 373, 377, 393, 402, 413, 421, 422, 453, 461, 462

Offset

1,2

Comments

Or, concatenating T(1) and T(k) produces a prime, or, concatenating A000217(1) and A000217(k) produces a prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

T(2)=3, 13 is prime, so 2 is a term;
T(13)=91, 191 is prime, so 13 is a term;
T(17)=153, 1153 is prime, so 17 is a term.

Mathematica

Rest[Select[Range[600], PrimeQ[FromDigits[Join[{1}, IntegerDigits[(# (#+1))/2]]]]&]] (* Harvey P. Dale, Apr 15 2009 *)
trprQ[n_]:=Module[{tr=(n(n+1))/2}, PrimeQ[10^IntegerLength[tr]+tr]]; Select[ Range[ 500], trprQ] (* Harvey P. Dale, Aug 04 2019 *)

Crossrefs

Cf. A000217, A158844, A158750.

Sequence in context: A258317 A318911 A065245 * A163786 A153507 A124277

Adjacent sequences: A158842 A158843 A158844 * A158846 A158847 A158848

Keyword

nonn,base

Author

Zak Seidov, Mar 28 2009

Extensions

First term (1) prepended by Harvey P. Dale, Aug 04 2019

Status

approved