1,1

This is the 4th row of a table which begins as follows.

A[k,n] = Numbers n such that the sum of the digits of k^n is prime.

k..A[k,n]

1..none

2..A076203

3..none (3 | sum of digits)

4..2, 4, 5, 6, 9, 10, 12, 14, 15, 17, ... this sequence

5..1, 2, 4, 5, 6, 7, 19, ...

Numbers k such that A007953(A000302(k)) is in A000040.

a(1) = 2 because digit sum(4^2) = digit sum(16) = 1+6 = 7.

a(2) = 4 because digit sum(4^4) = digit sum(256) = 13.

a(3) = 5 because digit sum(4^5) = digit sum(1024) = 7.

a(4) = 6 because digit sum(4^6) = digit sum(4096) = 19.

a(5) = 9 because digit sum(4^9) = digit sum(262144) = 19.

a(6) = 10 because digit sum(4^10) = digit sum(1048576) = 31.

a(7) = 12 because digit sum(4^12) = digit sum(16777216) = 37.

a(8) = 14 because digit sum(4^14) = digit sum(268435456) = 43.

a(9) = 15 because digit sum(4^15) = digit sum(1073741824) = 37.

a(10) = 17 because digit sum(4^17) = digit sum(17179869184) = 61.

sd:=proc(n) options operator, arrow: add(convert(n, base, 10)[j], j=1..nops(convert(n, base, 10))) end proc: a:=proc(n) if isprime(sd(4^n)) = true then n else end if end proc: seq(a(n), n=1..150); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2007

Select[Range[500], PrimeQ[Plus @@ IntegerDigits[4^# ]] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 20 2007

Cf. A000040, A000302, A007953, A076203.

Sequence in context: A076354 A069470 A047435 this_sequence A125297 A143072 A089648

Adjacent sequences: A132788 A132789 A132790 this_sequence A132792 A132793 A132794

base,easy,less,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 17 2007

More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 20 2007