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A076704
Numbers k of the form p^q where both p and q are prime and all digits of k are odd.
3
9, 1331, 357911, 5177717, 5735339, 9393931, 17171515157399, 335571975137771, 7979737131773191, 13337513771953951, 13137917533317175739371379, 33159599371999557199755557, 1593395573971551557179777111133, 131755773357537951113179771515713, 315113377779977515359339551539771
OFFSET
1,1
COMMENTS
Up to 10^17, there are only 10 odd-digit prime powers of prime numbers. a(1) = 3^2, a(2) = 11^3, a(3) = 71^3, a(4) = 173^3, a(5) = 179^3, a(6) = 211^3, a(7) = 25799^3, a(8) = 69491^3, a(9) = 199831^3, and a(10) = 237151^3.
The only candidates for even-digit prime powers of prime numbers are of the form 2^n, and below 2^10000 there are only 2, 4, 8, 64, and 2048, two of which are not raised to prime powers.
a(11) <= 13137917533317175739371379 and a(12) <= 33159599371999557199755557. - Jinyuan Wang, Mar 02 2020
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..36 (terms < 10^57)
MATHEMATICA
pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^17]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^17]]]}]]]; Do[ If[ Union[ OddQ[ IntegerDigits[ pp[[n]]]]] == {True}, Print[ pp[[n]]]], {n, 1, Length[pp]}]
PROG
(PARI) lista(nn) = {my(k, v=List([])); forprime(p=2, nn, forprime(q=2, logint(nn, p), if(Set(digits(k=p^q)%2)==[1], listput(v, k)))); Set(v); } \\ Jinyuan Wang, Mar 02 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Oct 26 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Oct 31 2002
Corrected and edited by Elliott Line, Jul 11 2013
Better definition from Jon E. Schoenfield, Nov 19 2018
Terms a(11) and beyond from Giovanni Resta, Mar 03 2020
STATUS
approved