A158051 Primes in which a digit is square of another digit in the same prime.

11, 101, 113, 131, 139, 151, 181, 191, 193, 211, 239, 241, 293, 311, 349, 359, 379, 389, 397, 421, 439, 593, 739, 811, 839, 911, 937, 953, 983, 1009, 1013, 1019, 1021, 1031, 1039, 1051, 1061, 1091, 1093, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171

Offset: 1

Author

Parthasarathy Nambi, Mar 11 2009

Keywords

• base
• nonn

Comments

There are << x^k primes missing from this sequence up to x, where k = log 6/log 10 = 0.7781.... - Charles R Greathouse IV, Nov 29 2022

Examples

			953 is a prime in which a digit is square of another digit.
		

Links

• Chris Caldwell, The First 1,000 Primes

Crossrefs

Subsequence of A158290.

Programs

Mathematica

Select[Prime[Range[200]],AnyTrue[Sort/@Subsets[IntegerDigits[#],{2}],#[[1]]^2 == #[[2]]&]&] (* Harvey P. Dale, Nov 29 2022 *)

Python

from sympy import isprime
def ok(n): s = str(n); return (s.count("0") > 1 or s.count("1") > 1 or ("2" in s and "4" in s) or ("3" in s and "9" in s)) and isprime(n)
print([k for k in range(1172) if ok(k)]) # Michael S. Branicky, Nov 29 2022

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Nov 29 2022

Extensions

Corrected and extended by Harvey P. Dale, Nov 29 2022