A330385 Add the odd terms and subtract the even ones, the result must always be a square. This is the lexicographically earliest sequence of distinct positive integers with this property.

1, 3, 4, 9, 7, 12, 5, 8, 15, 16, 25, 11, 13, 24, 39, 17, 19, 21, 23, 44, 36, 28, 20, 33, 40, 27, 32, 45, 48, 35, 85, 72, 51, 64, 133, 87, 60, 29, 31, 105, 123, 84, 41, 43, 141, 96, 47, 49, 159, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 164, 156

Offset

1,2

Comments

This sequence is a variant of A329544.

All terms belong to A042965.

Links

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

Rémy Sigrist, Scatterplot of the first 5000000 terms

Example

The first terms, alongside the corresponding running totals, are:
  n   a(n)  t(n)
  --  ----  --------
   1     1   1 = 1^2
   2     3   4 = 2^2
   3     4   0 = 0^2
   4     9   9 = 3^2
   5     7  16 = 4^2
   6    12   4 = 2^2
   7     5   9 = 3^2
   8     8   1 = 1^2
   9    15  16 = 4^2
  10    16   0 = 0^2
  11    25  25 = 5^2

Prog

(PARI) s=t=0; for (n=1, 65, for (v=1, oo, if (!bittest(s, v) && issquare(u=t-v*(-1)^v), print1 (v", "); s+=2^v; t=u; break)))

Crossrefs

Cf. A000290, A042965, A329544, A330386 (running totals).

Sequence in context: A356541 A062319 A285265 * A178590 A022463 A378116

Adjacent sequences: A330382 A330383 A330384 * A330386 A330387 A330388

Keyword

nonn,look

Author

Rémy Sigrist, Dec 12 2019

Status

approved