A230665 - OEIS

%I #27 Jan 23 2014 15:41:55

%S 11,13,41,37,47,67,53,79,59,109,107,109,139,151,167,173,229,263,271,

%T 307,397,389,409,421,383,463,439,419,487,467,491,569,599,647,653,613,

%U 677,683,757,751,727,853,821,881,907,937,1021,1061,1033,1087,1193,1249,1229

%N Primes which are equal to the digit sum of 38^n, in the order that they are found.

%C The expression k^n with 1 < n < 100 generates more primes with k=38 than any other value of k in the range 1 < k < 100. Hence, 38 is considered for this sequence such that digit sum of 38^n is prime.

%C 38 generates 37 primes in that range of k. The 404 is the next better prime generator, with 40 primes. Next two records are 278249 with 43 primes and 458635073 with 45. (No more records to 10^9.) - _Charles R Greathouse IV_, Jan 21 2014

%H K. D. Bajpai, <a href="/A230665/b230665.txt">Table of n, a(n) for n = 1..4000</a>

%e a(3)= 41: 38^5= 79235168: The digital sum= 7+9+2+3+5+1+6+8= 41 which is prime.

%e a(6)= 67: 38^8= 4347792138496: The digital sum= 4+3+4+7+7+9+2+1+3+8+4+9+6= 67 which is prime.

%p with(StringTools):KD := proc() local a,b; a:= 38^n ;b:=add( i,i = convert((a), base, 10))(a);if isprime(b) then  return (b);fi;end: seq(KD(),n=1..500);

%t Select[Table[Total[IntegerDigits[38^k]], {k,100}], PrimeQ]

%o (PARI) list(maxx)={cnt=0;q=38;new=1;n=1;while(n<maxx,new=new*q;

%o myval=sumdigits(new);if(isprime(myval), print(myval);cnt++); n++); } \\ _Bill McEachen_, Nov 10 2013

%Y Cf. A007953 (digit sum of n).

%Y Cf. A062604 (primes: 38^n-37^n).

%Y Cf. A175527 (digit sum of 13^n).

%K nonn,base,less

%O 1,1

%A _K. D. Bajpai_, Oct 27 2013