A125239 Smallest prime divisor of 10*T(n)+1 = 5*n*(n+1)+1, where T(n) = 1 + 2 + ... + n.

11, 31, 61, 101, 151, 211, 281, 19, 11, 19, 661, 11, 911, 1051, 1201, 1361, 1531, 29, 1901, 11, 2311, 2531, 11, 3001, 3251, 3511, 19, 31, 19, 4651, 11, 5281, 31, 11, 6301, 6661, 79, 7411, 29, 59, 79, 11, 9461, 9901, 11, 19, 29, 19, 12251, 41, 89, 13781, 11

Offset

1,1

Comments

All divisors of 10*T(n)+1 are congruent to 1 or -1 modulo 10; that is, they end in the decimal digit 1 or 9.

Links

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

Nick Hobson, Triangular Numbers.

Example

10*T(9) + 1 = 5*9*10 + 1 = 451 = 11*41, so a(9) = 11.

Mathematica

FactorInteger[#][[1, 1]]&/@(10*Accumulate[Range[60]]+1) (* Harvey P. Dale, Dec 12 2011 *)

Prog

(PARI) a(n) = if(n<1, 0, factor(5*n*(n+1)+1)[1, 1])

Crossrefs

Cf. A000217, A062786, A090562, A124989.

Sequence in context: A040162 A113747 A202007 * A062786 A090562 A174244

Adjacent sequences: A125236 A125237 A125238 * A125240 A125241 A125242

Keyword

easy,nonn

Author

Nick Hobson, Nov 25 2006

Status

approved