cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A234011 The sums of 2 consecutive odious numbers (A000069).

Original entry on oeis.org

3, 6, 11, 15, 19, 24, 27, 30, 35, 40, 43, 47, 51, 54, 59, 63, 67, 72, 75, 79, 83, 86, 91, 96, 99, 102, 107, 111, 115, 120, 123, 126, 131, 136, 139, 143, 147, 150, 155, 160, 163, 166, 171, 175, 179, 184, 187, 191, 195, 198, 203, 207, 211, 216, 219, 222, 227, 232, 235, 239, 243, 246
Offset: 1

Views

Author

Gerasimov Sergey, Dec 27 2013

Keywords

Comments

The union of A131323(k) and (A225822(m)+(-1)^m).
All even numbers in this sequence are evil numbers (A001969).
It seems that A233388(n) = a(A091785(n)).

Links

Crossrefs

Cf. A000069, A003159 (indices of odd numbers in A234011), A036554 (indices of even numbers in A234011), A131323 (odd sums of 2 successive odious or 2 successive evil numbers), A233388 (odious numbers in A234011), A234431 (sums of 2 consecutive evil numbers), A017101, A091785, A225822, A227930, A233388.

Programs

Formula

a(n) = A000069(n) + A000069(n + 1).
4n - 2 <= a(n) <= 4n. - Charles R Greathouse IV, Dec 29 2013
a(2n+1) = 8n + 3 = A017101(n). - Ralf Stephan, Dec 31 2013

Extensions

Terms recomputed and checked by Antti Karttunen, Dec 29 2013

A234648 Even sums of 2 consecutive odious numbers (A000069).

Original entry on oeis.org

6, 24, 30, 40, 54, 72, 86, 96, 102, 120, 126, 136, 150, 160, 166, 184, 198, 216, 222, 232, 246, 264, 278, 288, 294, 312, 326, 344, 350, 360, 374, 384, 390, 408, 414, 424, 438, 456, 470, 480, 486, 504, 510, 520, 534, 544, 550, 568, 582, 600, 606, 616, 630
Offset: 1

Views

Author

Gerasimov Sergey, Dec 29 2013

Keywords

Comments

All the terms in this sequence are evil numbers (A001969).

Links

Crossrefs

Intersection of A005843 and A234011.
Cf. A000069, A001969, A036554, A131323, A225822.

Programs

  • Mathematica
    odQ[n_] := OddQ @ DigitCount[n, 2, 1]; Select[Plus @@@ Partition[Select[ Range[320], odQ], 2, 1], EvenQ] (* Amiram Eldar, Aug 31 2020 *)

Formula

a(n) = A234011(A036554(n)) = A225822(n) + (-1)^n.

A386987 For n >= 2, a(n) is the least r >= 1 such that T(n - r) + ... + T(n - 1) = T(n + 1) + ... + T(n + r) where T(i) is A010060(i).

Original entry on oeis.org

2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3
Offset: 2

Views

Author

Ctibor O. Zizka, Aug 12 2025

Keywords

Comments

a(n) is from {1, 2, 3, 4}.

Examples

			For n = 6: T(6 - r) + ... + T(5) = T(7) + ... + T(6 + r) is true for the least r = 4  because A010060(2) + A010060(3) + A010060(4) + A010060(5) = A010060(7) + A010060(8) + A010060(9) + A010060(10), thus a(6) = 4.

Crossrefs

Cf. A010060, A056196, A079523, A081706, A131323, A225822, A249034.

Programs

  • Mathematica
    a[n_] := Module[{s = 0, r = 1}, While[r <= n && (r == 1 || s != 0), s += (ThueMorse[n - r] - ThueMorse[n + r]); r++]; r-1]; Array[a, 100, 2] (* Amiram Eldar, Aug 12 2025 *)

Formula

a(A081706(n) + 1) = 1.
a(2*A079523(n)) = 2.
a(A249034(n))= 2.
a(A225822(n)) = 3.
a(A056196(n)) = 3.
a(2*A131323(n)) = 4.
a(2*A249034(n) - 1) = 4.
Showing 1-3 of 3 results.

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