A167740 Primes that become squares when prefixed with a 7.

29, 569, 1289, 7841, 62129, 306209, 436529, 502121, 634169, 667361, 935489, 1723961, 1927361, 2131049, 2437121, 2539289, 2948681, 3153809, 3564929, 4080449, 5116889, 5846681, 6160529, 6790169, 7316849, 7845329, 8269409, 8481881, 8694641, 8801129, 9869969

Offset: 1

Author

Claudio Meller, Nov 10 2009

Keywords

• base
• nonn

Links

• Vincenzo Librandi and David A. Corneth, Table of n, a(n) for n = 1..17124 (first 45 terms from Vincenzo Librandi)

Crossrefs

Cf. A167734, A167735, A167736, A167737, A167738, A167739, A167741.

Programs

Mathematica

Select[Prime[Range[10000]], IntegerQ[Sqrt[FromDigits[Join[{7}, IntegerDigits[#]]]]]&] (* G. C. Greubel, Jun 23 2016 *)

PARI

isok(n) = isprime(n) && issquare(n + 7*10^(length(Str(n)))) \\ Michel Marcus, Aug 05 2013

PARI

\\ terms upto 10^n
upto(n) = {my(sqrt71 = sqrt(7.1), sqrt80 = sqrt(8.0),r); for(k=2, n, for(j = ceil((sqrt71 * sqrt(10^k))), floor(sqrt80 * sqrt(10^k)), r = j^2%10^k; if(isprime(r), print1(r", "))))} \\ David A. Corneth, Jun 24 2016

Extensions

More terms from Michel Marcus, Aug 05 2013

Definition modified by Harvey P. Dale, Nov 12 2021