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
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
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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
Comments