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A132791 Numbers k such that the sum of the digits of 4^k is prime. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A125297 A194469 A143072

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

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Last modified April 10 06:16 EDT 2020. Contains 333392 sequences. (Running on oeis4.)