A057659 Prime numbers whose square is composed of just two different decimal digits.

5, 7, 11, 109, 173, 81619

Offset

1,1

Comments

Conjectured to be a finite sequence.

No further terms up to prime(1000000)=15485863. - Harvey P. Dale, Mar 20 2011

References

Related to the Unsolved problem F24, p. 262, of the UPiNT by R. K. Guy

Links

Table of n, a(n) for n=1..6.

Example

81619^2 = 6661661161.

Maple

filter:= p -> nops(convert(convert(p^2, base, 10), set))= 2:
select(filter, [seq(ithprime(i), i=1..10^5)]); # Robert Israel, Feb 11 2025

Mathematica

Select[Prime[Range[10000]], Count[DigitCount[#^2], 0] ==8&] (* Harvey P. Dale, Mar 20 2011 *)

Prog

(PARI) select(x->#Set(digits(x^2))==2, primes(10000)) \\ Michel Marcus, Feb 11 2025

Crossrefs

Subsequence of A016069.

Cf. A235154.

Sequence in context: A086140 A104387 A133761 * A098040 A263880 A082565

Adjacent sequences: A057656 A057657 A057658 * A057660 A057661 A057662

Keyword

nonn,base,more

Author

Carlos Rivera, Oct 15 2000

Status

approved