A355369 - OEIS

%I #8 Jun 30 2022 14:45:12

%S 11,2,167,2,19,5,911,2,61,59,919,29,337,919,983,29,541,311,1721,359,

%T 757,419,877,61,59,151,16943,1637,1439,71,3739,557,443,1303,353,569,

%U 2381,97,2389,5519,617,1381,89,7,1103,733,409,521,499,283,911,709,5113,179,9157,3533,971,47,3191,3917

%N 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.

%H Robert Israel, <a href="/A355369/b355369.txt">Table of n, a(n) for n = 1..815</a>

%e 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.

%p P:= [seq(ithprime(i),i=1..10^5)]:

%p sd:= n -> convert(convert(n,base,10),`+`):

%p S:= map(sd, P):

%p f:= proc(n)

%p   local p,s,i;

%p   p:= mul(P[i],i=1..n);

%p   s:= add(S[i],i=1..n);

%p   for i from 1 to 10^5-n do

%p     if isprime(p+s) then return P[i] fi;

%p     p:= p/P[i]*P[i+n];

%p     s:= s - S[i]+S[i+n];

%p   od;

%p -1

%p end proc:

%p map(f, [$1..100]);

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jun 30 2022