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

1,1

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

Links

Table of n, a(n) for n=1..48.

Chris Caldwell, The First 1,000 Primes

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A158290.

Sequence in context: A240602 A117697 A305395 * A091366 A073064 A155075

Adjacent sequences: A158048 A158049 A158050 * A158052 A158053 A158054

Keyword

base,nonn

Author

Parthasarathy Nambi, Mar 11 2009

Extensions

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

Status

approved