A030083 Primes p such that all digits of p^2 appear in p.

1049, 17923, 49261, 81619, 94583, 100469, 100549, 102953, 107251, 110923, 125789, 149827, 184903, 256169, 279863, 285101, 289573, 298327, 370421, 406951, 459521, 471923, 472963, 492671, 493621, 497521, 499423, 502261, 504821, 569423, 582139, 597823, 631927

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Contains A050288.

Cf. A030084.

Programs

Maple

R:= NULL: count:= 0: p:= 2:
while count < 100 do
 p:= nextprime(p);
 if convert(convert(p^2,base,10),set) subset convert(convert(p,base,10),set) then
    count:= count+1; R:= R,p
 fi
od:
R; # Robert Israel, Nov 01 2023

Mathematica

Select[Prime[Range[52000]],SubsetQ[IntegerDigits[#],IntegerDigits[#^2]]&] (* Harvey P. Dale, Aug 12 2025 *)

Python

from sympy import isprime
def ok(n): return isprime(n) and set(str(n)) >= set(str(n**2))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Nov 01 2023

Extensions

Offset corrected by Robert Israel, Nov 01 2023