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Primes in the sequence A064491.
1

%I #15 Jul 30 2024 17:57:00

%S 2,7,71,73,811,821,823,883,937,947,953,977,983,997,1031,1033,1051,

%T 1063,1093,1103,1153,1171,1181,1193,1231,1277,1279,1289,1291,1297,

%U 1303,1321,1381,1427,1429,1439,1451,1453,1471,1481,1483,29599,29641,29683,29717

%N Primes in the sequence A064491.

%C 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?

%H Robert Israel, <a href="/A113866/b113866.txt">Table of n, a(n) for n = 1..4453</a>

%e 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

%p a:= 1: R:= NULL: count:= 0:

%p while count < 100 do

%p a:= a+numtheory:-tau(a);

%p if isprime(a) then count:= count+1; R:= R, a; fi

%p od:

%p R; # _Robert Israel_, Nov 14 2020

%t Select[NestList[#+DivisorSigma[0, #]&, 1,2535] ,PrimeQ] (* _James C. McMahon_, Jul 07 2024 *)

%Y Cf. A064491.

%K nonn,look

%O 1,1

%A _John L. Drost_, Jan 25 2006