A341899 - OEIS

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

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OFFSET

1,1

COMMENTS

First differs from A306920 at n = 13.

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

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

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.

PROG

(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)))

CROSSREFS

Cf. A306920, A344637, A344936, A344937.

Sequence in context: A214495 A162011 A123248 * A306920 A336481 A111477

Adjacent sequences: A341896 A341897 A341898 * A341900 A341901 A341902

KEYWORD

nonn,base

AUTHOR

Felix Fröhlich, Jun 04 2021

STATUS

approved