A052042 Primes that lack the digit zero in the decimal expansion of their squares.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 61, 67, 73, 79, 83, 89, 107, 109, 113, 127, 131, 137, 139, 157, 163, 167, 173, 181, 191, 193, 211, 223, 227, 229, 233, 239, 263, 269, 271, 277, 281, 293, 307, 311, 313, 337, 359, 367, 373, 379, 383, 389, 409, 419, 421, 431

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Examples

			The primes 47, 53 and 71 are not in the sequence because 47^2=2209, 53^2=2809 and 71^2=5041 contain zeros in their decimal representation.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Squares: A052043, A052040, A052041. Cubes: A051750, A051751, A051832, A051833.

Cf. A245576.

Programs

Mathematica

fQ[n_] := DigitCount[n^2][[-1]] == 0; Select[Prime@ Range@ 80, fQ] (* Robert G. Wilson v, Aug 22 2012 *)

PARI

{p=2;for(k=1,10^2,if(vecmin(digits(p^2))>0,
print1(p", "));p=nextprime(1+p))}\\ Zak Seidov, Dec 24 2014

Formula

a(n) = sqrt(A052043(n)). - Zak Seidov, Dec 27 2014