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

Author

Zak Seidov, Jun 24 2003

Keywords

• easy
• nonn
• base
• changed

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

Examples

			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.
		

Links

• Robert Price, Table of n, a(n) for n = 0..5000
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A032734, A069691.

Programs

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

Formula

If n is prime, then a(n) = n, else a(n) = A069691(n). - Michel Marcus, Oct 05 2013

Extensions

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