A100272 -id:A100272 - cp's OEIS frontend

A331525 a(n) is the least positive k such that A100272(n) - k^2 is a fifth power.

1, 2, 4, 6, 3, 10, 9, 14, 15, 8, 20, 14, 16, 24, 20, 26, 22, 27, 26, 3, 5, 13, 15, 36, 34, 23, 40, 27, 33, 44, 37, 51, 54, 45, 56, 18, 58, 24, 53, 63, 55, 57, 64, 66, 36, 69, 42, 63, 74, 75, 73, 82, 84, 66, 86, 90, 93, 92, 31, 94, 35, 78, 99, 49, 84, 100, 97

Offset: 1

Rémy Sigrist, Jan 19 2020

nonn

			The first terms, alongside A100272(n), are:
  n   a(n)  A100272(n)
  --  ----  ----------------
   1     1    2 =  1^2 + 1^5
   2     2    5 =  2^2 + 1^5
   3     4   17 =  4^2 + 1^5
   4     6   37 =  6^2 + 1^5
   5     3   41 =  3^2 + 2^5
   6    10  101 = 10^2 + 1^5
   7     9  113 =  9^2 + 2^5
   8    14  197 = 14^2 + 1^5
   9    15  257 = 15^2 + 2^5
  10     8  307 =  8^2 + 3^5

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A331525

See A331435 for similar sequences.

Cf. A000584, A100272.

PARI
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A100292 Numbers of the form a^5 + b^2 with a, b > 0.

Original entry on oeis.org

2, 5, 10, 17, 26, 33, 36, 37, 41, 48, 50, 57, 65, 68, 81, 82, 96, 101, 113, 122, 132, 145, 153, 170, 176, 197, 201, 226, 228, 244, 247, 252, 257, 259, 268, 279, 288, 290, 292, 307, 321, 324, 325, 343, 356, 362, 364, 387, 393, 401, 412, 432, 439, 442, 468, 473

Offset: 1

T. D. Noe, Nov 18 2004

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A100272 (primes of the form a^5 + b^2).

Cf. A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4), A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).

lst={}; Do[p=a^5+b^2; If[p<1000, AppendTo[lst, p]], {a, 16}, {b, 1024}]; Union[lst]

is(n, m=5)=for(a=1, sqrtnint(n-1, m), issquare(n-a^m) && return(a)) \\ M. F. Hasler, Apr 25 2018

cp's OEIS Frontend

A331525 a(n) is the least positive k such that A100272(n) - k^2 is a fifth power.

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