A331524 a(n) is the least positive k such that A006686(n) - k^8 is an eighth power.

1, 1, 1, 5, 3, 7, 2, 8, 3, 8, 9, 13, 4, 4, 17, 7, 17, 2, 8, 3, 5, 20, 7, 11, 17, 8, 23, 19, 10, 20, 3, 11, 17, 10, 22, 19, 14, 22, 17, 21, 25, 11, 13, 23, 27, 8, 32, 25, 33, 6, 25, 35, 7, 23, 31, 10, 37, 16, 18, 39, 5, 7, 42, 41, 30, 36, 5, 11, 8, 18, 30, 36

Offset: 1

Author

Rémy Sigrist, Jan 19 2020

Keywords

• nonn

Examples

			The first terms, alongside A006686(n), are:
  n   a(n)  A006686(n)
  --  ----  -----------------------
   1     1           2 = 1^8 +  1^8
   2     1         257 = 1^8 +  2^8
   3     1       65537 = 1^8 +  4^8
   4     5     2070241 = 5^8 +  6^8
   5     3   100006561 = 3^8 + 10^8
   6     7   435746497 = 7^8 + 12^8
   7     2   815730977 = 2^8 + 13^8
   8     8   832507937 = 8^8 + 13^8
   9     3  1475795617 = 3^8 + 14^8
  10     8  2579667841 = 8^8 + 15^8
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A331524

Crossrefs

See A331435 for similar sequences.

Cf. A001016, A006686.

Programs

PARI

See Links section.