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

Author

Rémy Sigrist, Dec 12 2019

Keywords

• nonn
• look

Comments

This sequence is a variant of A329544.

All terms belong to A042965.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 5000000 terms

Crossrefs

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

Programs

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)))