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

1,1

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, ...

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A000302, A007953, A076203.

Sequence in context: A332570 A047435 A331085 * A352320 A352508 A125297

Adjacent sequences: A132788 A132789 A132790 * A132792 A132793 A132794

Keyword

base,easy,less,nonn

Author

Jonathan Vos Post, Nov 17 2007

Extensions

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

Edited by Jon E. Schoenfield, May 11 2019

Status

approved