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%I #23 Feb 21 2024 10:53:23
%S 1,4,5,7,8,10,12,18,19,20,23,24,25,28,29,30,31,34,35,38,39,40,48,52,
%T 63,66,68,69,72,81,87,89,92,94,96,97,99,101,119,121,125,132,133,145,
%U 146,148,153,158,162,164,165,167,175,177,184,187,191
%N Numbers n such that the sum of the digits of 2^n is prime.
%H Zak Seidov, <a href="/A076203/b076203.txt">Table of n, a(n) for n = 1..1000.</a>
%e For n=7, 2^7=128 and 1+2+8=11, a prime. For n=23, 2^23=8388608 having the sum of its digits equaling 41.
%t a={};For[n=1,n<200, n++, If[PrimeQ[Plus @@ IntegerDigits[2^n]],AppendTo[a, n]]];a (* _Stefan Steinerberger_, Jun 08 2007 *)
%t Select[Range[200],PrimeQ[Total[IntegerDigits[2^#]]]&] (* _Harvey P. Dale_, Jan 30 2018 *)
%o (R)
%o library(gmp); digsum<-function(x) sum(as.numeric(unlist(strsplit(as.character(x),split=""))))
%o which(isprime(sapply(as.character(as.bigz(2)^(1:100)),digsum))>0) #_Christian N. K. Anderson_, Apr 29 2013
%K nonn,base
%O 1,2
%A _Zak Seidov_, Nov 02 2002
%E More terms from _Stefan Steinerberger_, Jun 08 2007