A256970 Smallest prime divisor of 4*n^2+1.

5, 17, 37, 5, 101, 5, 197, 257, 5, 401, 5, 577, 677, 5, 17, 5, 13, 1297, 5, 1601, 5, 13, 29, 5, 41, 5, 2917, 3137, 5, 13, 5, 17, 4357, 5, 13, 5, 5477, 53, 5, 37, 5, 7057, 13, 5, 8101, 5, 8837, 13, 5, 73, 5, 29, 17, 5, 12101, 5, 41, 13457, 5

Offset: 1

Author

N. J. A. Sloane, Apr 19 2015

Keywords

• nonn

Comments

a(n) = A020639(A053755(n)).

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

References

• Richard Friedberg, An Adventurer's Guide to Number Theory, McGraw-Hill, NY, 1968.
• Popular Computing (Calabasas, CA), Friedberg's Sequence, Vol. 5 (No. 46, Jan 1977), page PC46-2.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053755, A256971, A020639.

A bisection of A125256.

Programs

Haskell

a256970 = a020639 . a053755  -- Reinhard Zumkeller, Apr 20 2015

Mathematica

Table[FactorInteger[4*n^2+1][[1,1]],{n,59}] (* Ivan N. Ianakiev, Apr 20 2015 *)

PARI

a(n) = factor(4*n^2+1)[1,1]; \\ Michel Marcus, Apr 20 2015