A135376 a(n) is the smallest prime that does not divide n(n+1)/2.

2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 11, 2, 2, 5, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 11, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 5, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 11, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 5, 2, 2, 7, 3, 2, 2, 3

Offset: 1

Author

Leroy Quet, Dec 09 2007

Keywords

• nonn

Comments

The sums of the first 10^k terms, for k = 1, 2, ..., are 28, 354, 3596, 36026, 360402, 3604134, 36041392, 360413970, 3604140072, 36041400856, ... . Apparently, the asymptotic mean of this sequence is limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3.604140... . - Amiram Eldar, Sep 10 2022

Examples

			The 11th triangular number is 66 = 2*3*11. 5 is the smallest prime that is coprime to 66, so a(11) = 5.
		

Links

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

Crossrefs

Cf. A000217, A053669, A053670.

Programs

Maple

A135376 := proc(n) local T,p ; T := n*(n+1)/2 ; p := 2 ; while T mod p = 0 do p := nextprime(p) ; od: RETURN(p) ; end: seq(A135376(n),n=1..120) ; # R. J. Mathar, Dec 11 2007

Mathematica

a = {}; For[n = 1, n < 80, n++, j = 1; While[Mod[n*(n + 1)/2, Prime[j]] == 0, j++ ]; AppendTo[a, Prime[j]]]; a (* Stefan Steinerberger, Dec 10 2007 *)
sp[n_]:=Module[{p=2},While[Mod[n,p]==0,p=NextPrime[p]];p]; sp[#]&/@ Accumulate[ Range[110]] (* Harvey P. Dale, Jul 26 2018 *)

Formula

a(4n+1) = a(4n+2) = 2 for all nonnegative integers n.

a(n) = A053670(n) for all n congruent to 0 or 3 (mod 4).

a(n) = A053669(A000217(n)). - R. J. Mathar, Dec 11 2007

Extensions

More terms from Stefan Steinerberger and R. J. Mathar, Dec 10 2007