A084413 Smallest prime with "n" as central digit(s), or -1 if no such prime exists.

101, 113, 2, 3, 149, 5, 163, 7, 181, 191, 1103, 11, 1123, 13, 2141, 1151, 1163, 17, 1181, 19, 1201, 1213, 1223, 23, 1249, 1259, 2267, 1277, 1283, 29, 1301, 31, 1321, 2333, 2341, 2351, 1361, 37, 1381, 1399, 1409, 41, 1423, 43, 1447, 1451, 2467, 47, 1481

Offset

0,1

Comments

For n=5620 and n=7358, adding only one digit to both sides do not result in any prime. - Robert Price, Sep 16 2023

Links

Robert Price, Table of n, a(n) for n = 0..5000

Index entries for primes involving decimal expansion of n

Formula

If n is prime, then a(n) = n, else a(n) = A084414(n). - Michel Marcus, Oct 05 2013

Example

a(1)=113 because 113 is the smallest prime with "1" as central digit.
a(10)=1103 because 1103 is the smallest prime with "10" as central digits.

Prog

(PARI) findex(n) = {for (i = 1, 9, forstep (j=1, 9, 2, v = j + 10*n + i*10^(1+length(Str(n))); if (isprime(v), return (v)); ); ); }
a(n) = if (isprime(n), n, findex(n)); \\ code assumes only 1 digit on each side of 'n' will be necessary. See A032734 for numbers that need a better script. - Michel Marcus, Oct 05 2013

Crossrefs

Cf. A032734, A084414.

Sequence in context: A294743 A352439 A214527 * A248533 A069691 A084414

Adjacent sequences: A084410 A084411 A084412 * A084414 A084415 A084416

Keyword

easy,nonn,base

Author

Zak Seidov, Jun 24 2003

Extensions

Escape clause added by N. J. A. Sloane, Nov 11 2020

Status

approved