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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Cf. A245576.

Sequence in context: A154363 A049555 A281295 * A245576 A086472 A219669

Adjacent sequences: A052039 A052040 A052041 * A052043 A052044 A052045

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1999

Status

approved