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a(n) is the smallest prime p > 10 such that the resulting number when inserting strings of exactly n zeros are eachinserted between every pair allof adjacent digits ofthe presult is also a prime.

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N. J. A. Sloane: I rewrote the definition.

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a(n) is the smallest prime p > 10 such that the resulting number when inserting strings of exactly n zeros each between all adjacent digits of p is also prime.

nonn,changedbase

allocated for Felix Fröhlich

a(n) is the smallest prime p such that the resulting number when inserting strings of exactly n zeros each between all adjacent digits of p is also 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

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First differs from A306920 at n = 13.

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

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.

(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)))

Cf. A306920, A344637, A344936, A344937.

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Felix Fröhlich, Jun 04 2021

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allocated for Felix Fröhlich

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allocated for Vladimir Pletser

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allocated for Vladimir Pletser

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