A052043 Squares of primes lacking the digit zero in their decimal expansion.

4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 3481, 3721, 4489, 5329, 6241, 6889, 7921, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 24649, 26569, 27889, 29929, 32761, 36481, 37249, 44521, 49729, 51529, 52441, 54289

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Comments

Intersection of A052382 and A001248; A168046(a(n))*A064911(a(n))*A010052(a(n)) = 1. - Reinhard Zumkeller, Dec 01 2009

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Zerofree - _Reinhard Zumkeller_, Dec 01 2009

Crossrefs

Squares: A052042, A052040, A052041.

Cubes: A051750, A051751, A051832, A051833.

Programs

Mathematica

Select[Prime[Range[100]]^2,DigitCount[#,10,0]==0&] (* Harvey P. Dale, Mar 18 2012 *)

PARI

is(n)=my(d=digits(n));vecsort(d)[1]&&issquare(n,&n)&&isprime(n) \\ Charles R Greathouse IV, Jun 05 2013

Formula

a(n) = A052042(n)^2. - R. J. Mathar, Jul 23 2025