A226442 a(n) = smallest index m such that smallest prime factor of m-th triangular number is prime(n).

3, 2, 10, 13, 22, 298, 526, 37, 46, 58, 61, 73, 82, 3397, 2866, 106, 3481, 3721, 5293, 5041, 7081, 157, 166, 178, 193, 10201, 14317, 23326, 23761, 226, 17398, 262, 19042, 277, 24286, 38806, 313, 45802, 29893, 346, 358, 32761, 382, 46126, 52993, 397, 421, 68461

Offset

1,1

Comments

Or, smallest proper divisor of m-th triangular number is prime(n).

The curve is bimodal. Why? - T. D. Noe, Jun 07 2013

Links

Table of n, a(n) for n=1..48.

Formula

A069901(a(n)) = A000040(n).

Example

3rd triangular number, A000217(3) = 6 = 2*3, 2nd triangular number, A000217(2) = 3,
10th triangular number, A000217(10) = 55 = 5*11, 13th triangular number, A000217(13) = 91 =7*13.

Mathematica

nn = 50; t = Table[0, {nn}]; tri = 1; n = 1; found = 0; While[found < nn, n++; tri = tri + n; p = FactorInteger[tri][[1, 1]]; pi = PrimePi[p]; If[pi <= nn && t[[pi]] == 0, t[[pi]] = n; found++]]; t (* T. D. Noe, Jun 07 2013 *)

Crossrefs

Cf. A000040, A000217, A069901.

Sequence in context: A113980 A095675 A340806 * A300374 A256063 A006743

Adjacent sequences: A226439 A226440 A226441 * A226443 A226444 A226445

Keyword

nonn

Author

Zak Seidov, Jun 06 2013

Status

approved