A293958 Smallest odd prime divisor of (2n+1)^2 + 1.

5, 13, 5, 41, 61, 5, 113, 5, 181, 13, 5, 313, 5, 421, 13, 5, 613, 5, 761, 29, 5, 1013, 5, 1201, 1301, 5, 17, 5, 1741, 1861, 5, 2113, 5, 2381, 2521, 5, 29, 5, 3121, 17, 5, 3613, 5, 17, 41, 5, 4513, 5, 13, 5101, 5, 37, 5, 13, 61, 5, 17, 5, 73, 7321, 5, 13, 5, 53, 8581, 5, 13, 5, 9661, 9941, 5

Offset: 1

Author

N. J. A. Sloane, Nov 04 2017, following a suggestion from Zoran Sunic

Keywords

• nonn

Comments

If the map "x -> smallest odd prime divisor of n^2+1" is iterated, does it always terminate in the 2-cycle (5 <-> 13)? - Zoran Sunic, Oct 25 2017

A027862 is a subsequence. - David A. Corneth, Nov 04 2017

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

A bisection of A125256. Cf. A027862, A069894, A078701, A256970.

Programs

Mathematica

sod[n_]:=With[{fi=FactorInteger[n]},If[fi[[1,1]]==2,fi[[2,1]],fi[1,1]]]; sod/@(Range[3,151,2]^2+1) (* Harvey P. Dale, Dec 23 2023 *)

PARI

a(n) = factor((2*n+1)^2 + 1)[2,1]; \\ Michel Marcus, Nov 04 2017

Formula

a(n) = A078701(A069894(n)). - Michel Marcus, Nov 04 2017