A113866 Primes in the sequence A064491.

2, 7, 71, 73, 811, 821, 823, 883, 937, 947, 953, 977, 983, 997, 1031, 1033, 1051, 1063, 1093, 1103, 1153, 1171, 1181, 1193, 1231, 1277, 1279, 1289, 1291, 1297, 1303, 1321, 1381, 1427, 1429, 1439, 1451, 1453, 1471, 1481, 1483, 29599, 29641, 29683, 29717

Offset

1,1

Comments

if the sequence of iterates hits an odd square, then the succeeding f(n) is even. The iterates will remain even until f(n) is an even square, so the sequence grows slowly for a long time, then has big 'jumps'. Is the sequence infinite?

Links

Robert Israel, Table of n, a(n) for n = 1..4453

Example

If f(n) = n + tau(n), then the functional iterates of 7 are 7,9,12,18,24,32,38,42,50,56,64 and 71 which is prime so a(2)=7, a(3)=71

Maple

a:= 1: R:= NULL: count:= 0:
while count < 100 do
  a:= a+numtheory:-tau(a);
  if isprime(a) then count:= count+1; R:= R, a;  fi
od:
R; # Robert Israel, Nov 14 2020

Mathematica

Select[NestList[#+DivisorSigma[0, #]&, 1, 2535] , PrimeQ] (* James C. McMahon, Jul 07 2024 *)

Crossrefs

Cf. A064491.

Sequence in context: A366359 A319640 A260566 * A165978 A106917 A188665

Adjacent sequences: A113863 A113864 A113865 * A113867 A113868 A113869

Keyword

nonn,look

Author

John L. Drost, Jan 25 2006

Status

approved