A241246 Primes p such that the decimal expansion of its base 7 expansion converted to decimal is a square.

13, 19, 139, 313, 433, 571, 883, 1489, 3547, 10513, 11779, 14389, 20011, 25939, 27763, 30181, 32353, 42649, 44617, 45289, 46309, 47353, 48787, 55411, 65269, 65713, 96331, 111577, 120763, 129967, 151717, 157219, 201997, 216091, 281947, 292549, 322537, 339121, 373987, 397489, 420349, 432961, 460417, 475417, 478531, 506563, 582433, 591739, 599479, 753229, 778357, 857821, 861139, 887947, 968419, 1037089, 1062361, 1213651, 1246249

Offset: 1

Author

Zak Seidov, Apr 18 2014

Keywords

• nonn
• base

Comments

No terms are 0, 2, or 3 mod 7. - Charles R Greathouse IV, Apr 18 2014

Examples

			{13,19,139,313,433,571,883,1489,3547,10513,11779}_10 =
{16,25,256,625,1156,1444,2401,4225,13225,42436,46225}_7 =
{4,5,16,25,34,38,49,65,115,206,215}^2_10.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A090710, A065725.

Programs

PARI

is(n)=issquare(subst(Pol(digits(n,7)),'x,10)) && isprime(n) \\ Charles R Greathouse IV, Apr 18 2014

PARI

for(n=4,1e3,if(vecmax(v=digits(n^2))<7 && isprime(p= subst(Pol(v), 'x, 7)), print1(p", "))) \\ Charles R Greathouse IV, Apr 18 2014