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

Author

John L. Drost, Jan 25 2006

Keywords

• nonn
• look

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?

Examples

			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
		

Links

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

Crossrefs

Cf. A064491.

Programs

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 *)