A331435 a(n) is the least positive k such that A028916(n) - k^2 is a fourth power.

1, 2, 1, 6, 5, 4, 10, 11, 10, 14, 15, 1, 14, 5, 9, 20, 21, 24, 19, 4, 6, 26, 26, 12, 14, 29, 16, 31, 29, 22, 24, 31, 34, 1, 26, 5, 28, 35, 40, 19, 41, 39, 44, 38, 29, 45, 42, 4, 6, 35, 51, 16, 46, 20, 51, 54, 55, 56, 56, 30, 52, 54, 34, 36, 56, 58, 40, 9, 11

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A331435

Wikipedia, Friedlander-Iwaniec theorem

Example

The first terms, alongside A028916(n), are:
  n   a(n)  A028916(n)
  --  ----  ----------------
   1     1    2 =  1^2 + 1^4
   2     2    5 =  2^2 + 1^4
   3     1   17 =  1^2 + 2^4
   4     6   37 =  6^2 + 1^4
   5     5   41 =  5^2 + 2^4
   6     4   97 =  4^2 + 3^4
   7    10  101 = 10^2 + 1^4
   8    11  137 = 11^2 + 2^4
   9    10  181 = 10^2 + 3^4
  10    14  197 = 14^2 + 1^4

Prog

(PARI) See Links section.

Crossrefs

See A002331, A331521, A331522, A331523, A331524, A331525, A331526 and A331527 for similar sequences.

Cf. A000583, A028916.

Sequence in context: A359806 A346306 A021826 * A159927 A176443 A105225

Adjacent sequences: A331432 A331433 A331434 * A331436 A331437 A331438

Keyword

nonn

Author

Rémy Sigrist, Jan 18 2020

Status

approved