A123571 Smallest prime p such that p divides m^(m+1)+1, where m = (p-2n-1)/(2n).

13, 29, 79, 41, 41, 313, 421, 257, 541, 461, 1013, 673, 2341, 197, 661, 2113, 1361, 1009, 4447, 15161, 2857, 7789, 7499, 2113, 5101, 8269, 811, 9689, 1567, 1381, 2543, 31489, 3631, 23189, 9941, 10513, 16651, 21661, 84163, 5281, 13613, 1933, 22447, 23497, 2971

Offset

1,1

Comments

Corresponding m = {5,6,12,4,3,25,29,15,29,22,45,27,89,6,21,...}.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(1) = 13 because for m = (13-3)/2 = 5 prime 13 divides m^(m+1)+1 = 5^6+1 = 15626, but m^(m+1)+1 is not divisible by any prime p of the form p=2m+3 for m<5.

Maple

f:= proc(n) local p, m;
     p:= 1;
     do
       p:= nextprime(p);
       if p - 1 mod (2*n) <> 0 then next fi;
       m:= (p-2*n-1)/(2*n);
       if m &^ (m+1) + 1 mod p = 0 then return p fi;
     od
end proc:
map(f, [$1..100]); # Robert Israel, May 26 2026

Mathematica

s={}; Do[i=1; Until[p=Prime[i]; m=(p-2n-1)/(2n); Divisible[m^(m+1)+1, p], i++]; AppendTo[s, p], {n, 45}]; s (* James C. McMahon, Nov 23 2024 *)

Crossrefs

Cf. A177714.

Sequence in context: A217197 A141196 A269785 * A358742 A209989 A269515

Adjacent sequences: A123568 A123569 A123570 * A123572 A123573 A123574

Keyword

nonn,changed

Author

Alexander Adamchuk, Nov 12 2006

Extensions

More terms from R. J. Mathar, Jan 17 2008

a(44)-a(45) from James C. McMahon, Nov 23 2024

Status

approved