A245010 Numbers k such that k*prime(k) + 43 is a square.

2, 6, 13, 57, 1614, 3686, 735417, 252641277, 4849631998, 506364553163

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Example

       2 *        3 + 43 =       7^2;
       6 *       13 + 43 =      11^2;
      13 *       41 + 43 =      24^2;
      57 *      269 + 43 =     124^2;
    1614 *    13669 + 43 =    4697^2;
    3686 *    34501 + 43 =   11277^2;
  735417 * 11144513 + 43 = 2862842^2.

Mathematica

Select[Range[800000], IntegerQ[Sqrt[# Prime[#]+43]]&] (* Harvey P. Dale, Aug 04 2018 *)

Prog

(Sage)
L = primes_first_n(1000000)
[n for n in [1..999999] if is_square(n*L[n-1]+43)] # Tom Edgar, Jul 10 2014

Crossrefs

Cf. A106041, A106042.

Sequence in context: A284223 A241784 A211995 * A057243 A294130 A012470

Adjacent sequences: A245007 A245008 A245009 * A245011 A245012 A245013

Keyword

nonn,more

Author

Chai Wah Wu, Jul 09 2014

Extensions

a(8)-a(10) from Giovanni Resta, Oct 14 2019

Status

approved