A098961 Sums of two squares and divisible by 13.

13, 26, 52, 65, 104, 117, 130, 169, 208, 221, 234, 260, 325, 338, 377, 416, 442, 468, 481, 520, 533, 585, 637, 650, 676, 689, 754, 793, 832, 845, 884, 936, 949, 962, 1040, 1053, 1066, 1105, 1157, 1170, 1261, 1274, 1300, 1313

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = 13 * A001481(n+1) for n >= 1. - Joerg Arndt, Dec 03 2022

Example

Sums not divisible by 13 are shown in asterisks:
.
      |   1    4    9   16   25   36   49   64   81  100  121
  ----+------------------------------------------------------
    1 |   *    *    *    *   26    *    *   65    *    *    *
    4 |   *    *   13    *    *    *    *    *    *  104    *
    9 |   *   13    *    *    *    *    *    *    *    *  130
   16 |   *    *    *    *    *   52   65    *    *    *    *
   25 |  26    *    *    *    *    *    *    *    *    *    *
   36 |   *    *    *   52    *    *    *    *  117    *    *
   49 |   *    *    *   65    *    *    *    *  130    *    *
   64 |  65    *    *    *    *    *    *    *    *    *    *
   81 |   *    *    *    *    *  117  130    *    *    *    *
  100 |   *  104    *    *    *    *    *    *    *    *  221
  121 |   *    *  130    *    *    *    *    *    *  221    *

Maple

filter:= proc(n) local t, F;
  F:= select(t -> t[2]::odd, ifactors(n)[2]);
  andmap(t -> t[1] = 2 or t[1] mod 4 = 1, F);
end proc:
select(filter, [seq(i, i=13..10000, 13)]); # Robert Israel, Dec 02 2022

Mathematica

With[{nn=50}, Take[Union[Select[Total/@Subsets[Range[nn]^2, {2}], Divisible[ #, 13]&]], nn]] (* Harvey P. Dale, Aug 15 2014 *)

Crossrefs

Intersection of A001481 and A008595.

Cf. A094447.

Sequence in context: A044838 A033010 A019551 * A033897 A005029 A251149

Adjacent sequences: A098958 A098959 A098960 * A098962 A098963 A098964

Keyword

nonn

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Oct 22 2004

Status

approved