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A230665 Primes which are equal to the digit sum of 38^n, in the order that they are found. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base,less
AUTHOR
K. D. Bajpai, Oct 27 2013
STATUS
approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)