A132791 Numbers k such that the sum of the digits of 4^k is prime.

2, 4, 5, 6, 9, 10, 12, 14, 15, 17, 19, 20, 24, 26, 33, 34, 36, 46, 47, 48, 66, 73, 74, 79, 81, 82, 92, 98, 101, 103, 104, 106, 107, 110, 113, 118, 119, 126, 131, 132, 133, 136, 137, 143, 144, 145, 147, 151, 156, 158, 161, 164, 171, 181, 185, 192, 195, 198, 200, 204

Offset: 1

Author

Jonathan Vos Post, Nov 17 2007

Keywords

• base
• easy
• less
• nonn

Comments

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

A(j,k) = numbers k such that the sum of the digits of j^k is prime.

j | A(j,k)

--+-------------------------------------------------------

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, ...

Examples

			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.
		

Crossrefs

Cf. A000040, A000302, A007953, A076203.

Programs

Maple

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, Nov 24 2007

Mathematica

Select[Range[500], PrimeQ[Plus @@ IntegerDigits[4^# ]] &] (* Stefan Steinerberger, Nov 20 2007 *)

Formula

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

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Nov 20 2007

Edited by Jon E. Schoenfield, May 11 2019