A355369 a(n) is the least prime p such that the sum of the product of the n consecutive primes starting with p and the decimal digits of those primes is prime.

11, 2, 167, 2, 19, 5, 911, 2, 61, 59, 919, 29, 337, 919, 983, 29, 541, 311, 1721, 359, 757, 419, 877, 61, 59, 151, 16943, 1637, 1439, 71, 3739, 557, 443, 1303, 353, 569, 2381, 97, 2389, 5519, 617, 1381, 89, 7, 1103, 733, 409, 521, 499, 283, 911, 709, 5113, 179, 9157, 3533, 971, 47, 3191, 3917

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..815

Example

a(3) = 167 because the 3 primes starting with 167 are 167, 173 and 179, and 167*173*179+1+6+7+1+7+3+1+7+9 = 5171531 which is prime, and no smaller prime works.

Maple

P:= [seq(ithprime(i), i=1..10^5)]:
sd:= n -> convert(convert(n, base, 10), `+`):
S:= map(sd, P):
f:= proc(n)
  local p, s, i;
  p:= mul(P[i], i=1..n);
  s:= add(S[i], i=1..n);
  for i from 1 to 10^5-n do
    if isprime(p+s) then return P[i] fi;
    p:= p/P[i]*P[i+n];
    s:= s - S[i]+S[i+n];
  od;
-1
end proc:
map(f, [$1..100]);

Crossrefs

Sequence in context: A160464 A038316 A139311 * A140749 A010188 A309389

Adjacent sequences: A355366 A355367 A355368 * A355370 A355371 A355372

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jun 30 2022

Status

approved