A341899 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.

11, 19, 17, 13, 13, 23, 17, 17, 31, 13, 23, 41, 127, 61, 23, 13, 13, 67, 53, 89, 19, 227, 17, 29, 61, 151, 31, 37, 107, 53, 1741, 263, 167, 23, 31, 89, 61, 13, 43, 241, 53, 347, 1319, 19, 79, 419, 521, 19, 809, 677, 97, 97, 1223, 89, 13, 79, 67, 257, 17, 499

Offset: 1

Author

Felix Fröhlich, Jun 04 2021

Keywords

• nonn
• base

Comments

First differs from A306920 at n = 13.

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

Examples

			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.
		

Crossrefs

Cf. A306920, A344637, A344936, A344937.

Programs

PARI

eva(n) = subst(Pol(n), x, 10)
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)
a(n) = forprime(p=10, , if(ispseudoprime(insert_zeros(p, n)), return(p)))