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

Author

K. D. Bajpai, Oct 27 2013

Keywords

• nonn
• base
• less

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A007953 (digit sum of n).

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

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

Programs

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]

PARI

list(maxx)={cnt=0;q=38;new=1;n=1;while(nBill McEachen, Nov 10 2013