A091948 -id:A091948 - cp's OEIS frontend

A385993 a(n) is the number of distinct values appearing an odd number of times among A002487(0), ..., A002487(n).

1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 9, 10, 9, 8, 9, 10, 11, 10, 11, 10, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13

Offset: 0

Rémy Sigrist, Jul 14 2025

nonn

			Sequence begins:
  n   a(n)  A091948(n)
  --  ----  ----------
   0     1           1
   1     2           1
   2     1           2
   3     2           1
   4     3           3
   5     4           1
   6     3           2
   7     2           2
   8     1           4
   9     2           1
  10     3           3
  11     4           1
  12     5           3

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Rémy Sigrist, PARI program
Index entries for sequences related to Stern's sequences

Cf. A002487, A004171, A091948, A385991.

PARI
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a(n) = - Sum_{k = 1, n} (-1)^A091948(k).
abs(a(n+1) - a(n)) = 1.
a(n) = 1 iff n = 0 or n belongs to A004171.

A385996 a(n) is the least k such that some value appears n times among A002487(0), ..., A002487(k).

Original entry on oeis.org

0, 2, 4, 8, 16, 28, 34, 44, 52, 62, 68, 88, 104, 124, 130, 152, 184, 200, 232, 250, 260, 296, 328, 380, 388, 440, 472, 500, 524, 568, 632, 688, 764, 772, 848, 904, 968, 1012, 1030, 1064, 1144, 1232, 1288, 1424, 1534, 1538, 1648, 1784, 1840, 1928, 2008, 2038

Offset: 1

Rémy Sigrist, Jul 14 2025

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C++ program
Index entries for sequences related to Stern's sequences

See A385995 for the corresponding values.

Cf. A002487, A091948.

A091948(a(n)) = n (this is the first occurrence of n in A091948).

cp's OEIS Frontend

A385993 a(n) is the number of distinct values appearing an odd number of times among A002487(0), ..., A002487(n).

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