A230665 Primes which are equal to the digit sum of 38^n, in the order that they are found.

11, 13, 41, 37, 47, 67, 53, 79, 59, 109, 107, 109, 139, 151, 167, 173, 229, 263, 271, 307, 397, 389, 409, 421, 383, 463, 439, 419, 487, 467, 491, 569, 599, 647, 653, 613, 677, 683, 757, 751, 727, 853, 821, 881, 907, 937, 1021, 1061, 1033, 1087, 1193, 1249, 1229

Offset

1,1

Comments

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.

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

Links

K. D. Bajpai, Table of n, a(n) for n = 1..4000

Example

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

Maple

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);

Mathematica

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

Prog

(PARI) list(maxx)={cnt=0; q=38; new=1; n=1; while(n<maxx, new=new*q;
myval=sumdigits(new); if(isprime(myval), print(myval); cnt++); n++); } \\ Bill McEachen, Nov 10 2013

Crossrefs

Cf. A007953 (digit sum of n).

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

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

Sequence in context: A104151 A088263 A334556 * A132238 A132241 A329175

Adjacent sequences: A230662 A230663 A230664 * A230666 A230667 A230668

Keyword

nonn,base,less

Author

K. D. Bajpai, Oct 27 2013

Status

approved