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A158051
Primes in which a digit is square of another digit in the same prime.
1
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
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
KEYWORD
base,nonn
AUTHOR
Parthasarathy Nambi, Mar 11 2009
EXTENSIONS
Corrected and extended by Harvey P. Dale, Nov 29 2022
STATUS
approved