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A164336
a(1)=1. Thereafter, all terms are primes raised to the values of earlier terms of the sequence.
28
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
1,2
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
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Tetration
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 *)
PROG
(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
CROSSREFS
Sequence in context: A128603 A195943 A096165 * A348263 A115919 A038701
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 13 2009
EXTENSIONS
More terms from Hagen von Eitzen, Oct 03 2009
STATUS
approved