A164336 a(1)=1. Thereafter, all terms are primes raised to the values of earlier terms of the sequence.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227

Offset: 1

Author

Leroy Quet, Aug 13 2009

Keywords

• nonn

Comments

These are the values of exponent towers consisting completely of primes coefficients. (For example, p^(q^(r^(s^..))), all variables being primes.) This sequence first differs from the terms of A096165, after the initial 1 in this sequence, when 18446744073709551616 = 2^64 occurs in A096165 but not in this sequence.

A064372(a(n)) = 1. [Reinhard Zumkeller, Aug 27 2011]

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Tetration

Crossrefs

Cf. A096165, A164337.

Programs

Maple

q:= n-> is(n=1 or (l-> nops(l)=1 and q(l[1, 2]))(ifactors(n)[2])):
select(q, [$1..350])[];  # Alois P. Heinz, Dec 30 2020

Mathematica

Block[{a = {1}}, Do[If[Length@ # == 1 && MemberQ[a, First@ #], AppendTo[a, i]] &[FactorInteger[i][[All, -1]]], {i, 2, 227}]; a] (* Michael De Vlieger, Aug 31 2017 *)

PARI

L=1000;S=[1];SS=[];while(#S!=#SS, SS=S;S=[];for(i=1,#SS,forprime(p=2,floor(L^(1/SS[i])),S=concat(S,p^SS[i])));S=eval(setunion(S,SS)));vecsort(S) \\ Hagen von Eitzen, Oct 03 2009

Extensions

More terms from Hagen von Eitzen, Oct 03 2009