

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
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OFFSET

1,1


COMMENTS

Up to 10^17, there are only 10 odddigit 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 evendigit 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

Cf. A014261, A053810, A075308.
Sequence in context: A020261 A266864 A076442 * A117053 A270067 A213448
Adjacent sequences: A076701 A076702 A076703 * A076705 A076706 A076707


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



