%I #10 Jun 04 2021 23:52:28

%S 11,19,17,13,13,23,17,17,31,13,23,41,127,61,23,13,13,67,53,89,19,227,

%T 17,29,61,151,31,37,107,53,1741,263,167,23,31,89,61,13,43,241,53,347,

%U 1319,19,79,419,521,19,809,677,97,97,1223,89,13,79,67,257,17,499

%N a(n) is the smallest prime p > 10 such that when strings of n zeros are inserted between every pair of adjacent digits the result is also a prime.

%C First differs from A306920 at n = 13.

%C a(n) = A306920(n) if A306920(n) is < 100, i.e., is a two-digit number.

%e For n = 13: Inserting 13 zeros between all adjacent digits of 127 gives 10000000000000200000000000007, which is prime. Since 127 is the smallest prime where inserting exactly 13 zeros between all adjacent digits results in a number that is also prime, a(13) = 127.

%o (PARI) eva(n) = subst(Pol(n), x, 10)

%o insert_zeros(num, len) = my(d=digits(num), v=[]); for(k=1, #d-1, v=concat(v, concat([d[k]], vector(len)))); v=concat(v, d[#d]); eva(v)

%o a(n) = forprime(p=10, , if(ispseudoprime(insert_zeros(p, n)), return(p)))

%Y Cf. A306920, A344637, A344936, A344937.

%K nonn,base

%O 1,1

%A _Felix Fröhlich_, Jun 04 2021