A038370 Smallest prime with "n^2" as central digit(s).

101, 113, 149, 191, 1163, 1259, 1361, 1493, 2647, 1811, 11003, 11213, 11443, 11699, 11969, 12251, 12569, 12893, 13241, 13613, 14009, 14411, 14843, 15299, 15761, 16253, 16763, 17291, 27847, 18413, 19001, 29611, 210241, 110899, 311561, 112253, 112967

Offset: 0

Author

Zak Seidov, Jun 25 2003

Keywords

• easy
• nonn
• base
• changed

Comments

1195 is the smallest n such that 2 digits are needed on both sides of 1195^2 = 1428025 to give prime 10142802503. - Michel Marcus, Jun 05 2013

Crossrefs

Cf. A084413, A069691.

Programs

PARI

a(n) = {a = 1; ok = 0; while (!ok, lena = #Str(a); lenn = #Str(n^2); for (b=0, 10^lena - 1, p = b + 10^lena*n^2 + 10^(lenn+lena)*a; if (isprime(p), return (p)););a++;);} \\ Michel Marcus, Jun 05 2013

Extensions

Corrected by Robert G. Wilson v, Jun 27 2003

a(19) corrected by Sean A. Irvine, Jan 12 2021