A330385 -id:A330385 - cp's OEIS frontend

A330386 Running totals in A330385.

1, 4, 0, 9, 16, 4, 9, 1, 16, 0, 25, 36, 49, 25, 64, 81, 100, 121, 144, 100, 64, 36, 16, 49, 9, 36, 4, 49, 1, 36, 121, 49, 100, 36, 169, 256, 196, 225, 256, 361, 484, 400, 441, 484, 625, 529, 576, 625, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369

Offset: 1

Rémy Sigrist, Dec 12 2019

All terms are nonnegative squares.

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

Cf. A000290, A330385.

s=t=0; for (n=1, 58, for (v=1, oo, if (!bittest(s,v) && issquare(u=t-v*(-1)^v), print1 (t=u ", "); s+=2^v; break)))

a(n) = - Sum_{k = 1..n } A330385(k) * (-1)^A330385(k).

A330403 Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that t(0) = 0, and for any n > 0, at least one of t(n-1) - a(n) or t(n-1) + a(n) is a square; in case t(n-1) - a(n) is a square, set t(n) = t(n-1) - a(n), otherwise set t(n) = t(n-1) + a(n).

Original entry on oeis.org

1, 3, 4, 9, 5, 12, 7, 8, 15, 16, 25, 11, 13, 24, 21, 32, 20, 33, 40, 27, 28, 17, 19, 36, 39, 56, 45, 35, 48, 49, 64, 55, 72, 63, 23, 57, 60, 77, 65, 84, 44, 52, 29, 31, 68, 37, 80, 41, 76, 99, 81, 95, 51, 69, 87, 105, 123, 43, 88, 47, 92, 141, 96, 129, 111, 93

Offset: 1

Rémy Sigrist, Dec 13 2019

nonn

This sequence is a variant of A330385.

			The first terms, alongside t(n), are:
  n   a(n)  t(n)
  --  ----  ----
   0  N/A      0
   1     1     1
   2     3     4
   3     4     0
   4     9     9
   5     5     4
   6    12    16
   7     7     9
   8     8     1
   9    15    16
  10    16     0
  11    25    25
  12    11    36

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A330403

See A330401 for similar sequences.

Cf. A330385, A330422 (running totals).

PARI
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cp's OEIS Frontend

A330386 Running totals in A330385.

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