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URL: https://oeis.org/A355369

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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.
1
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
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
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Jun 30 2022
STATUS
approved