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.

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A262517 Odd terms in A259934.

Original entry on oeis.org

121, 125, 129, 113569, 113573, 113589, 113593, 113601, 113625, 113629, 113645, 113647, 113651, 113659, 113663, 113667, 113679, 113715, 113717, 113729, 113731, 113739, 113743, 113747, 113749, 113757, 113765, 113781, 113783, 113791, 113799, 113815, 113827, 113831, 113839, 113847, 113851, 113859, 113867, 113871, 113877, 113881, 113885, 113889, 113925, 113931, 113935, 113943, 113967, 113969, 113973, 113981, 113983, 113987, 113991
Offset: 1

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Author

Antti Karttunen, Sep 26 2015

Keywords

Comments

Odd terms of A259934 appear in separate runs, where the first term of each run is always an odd square, like 121 and 113569 are. See A262514 for the explanation.

Links

  • Antti Karttunen, Table of n, a(n) for n = 1..169794 (All odd terms as found from the data-file A259934 provided by _Max Alekseyev_, which contained terms up to A259934(397420670) = 9999999974.)

Crossrefs

Cf. A259934, A262514, A262516.
Cf. A262509, A262510 (subsequences?).

A266114 Least siblings in A263267-tree: numbers n for which there doesn't exist any k < n such that k - d(k) = n - d(n), where d(n) = A000005(n), the number of divisors of n.

Original entry on oeis.org

1, 3, 5, 6, 7, 8, 9, 11, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 56, 57, 58, 59, 61, 62, 65, 67, 68, 71, 72, 73, 74, 77, 79, 81, 82, 83, 84, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 109, 113, 114, 116, 118, 119, 120, 121, 123, 125, 127, 128
Offset: 1

Views

Author

Antti Karttunen, Dec 21 2015

Keywords

Comments

Sequence A082284 sorted into ascending order, with zeros removed.
At least initially, most of the odd squares (A016754) seem to be in A266114, while most of the even squares (A016742) seem to be in A266115. The first exceptions to this are 63^2 = 3969 = A266115(1296), and 20^2 = 400 = A266114(269).

Examples

			3 is present, as 3 - A000005(3) = 1, but there are no any number k less than 3 for which k - A000005(k) = 1. (Although there is a larger sibling 4, for which 4 - A000005(4) = 1 also). Thus 3 is a smallest children of 1 in a tree A263267 defined by edge-relation child - A000005(child) = parent.

Links

Crossrefs

Cf. A000005, A082284, A263267.
Cf. A266112 (characteristic function).
Cf. A266113 (least monotonic left inverse).
Cf. A266115 (complement).
Cf. A065091, A261089, A264988, A262509 (subsequences).
Cf. also A016742, A016754.

Formula

Other identities. For all n >= 1:
A266113(a(n)) = n.

A262513 Numbers where A049820 takes a unique value; numbers n for which A060990(A049820(n)) = 1.

Original entry on oeis.org

5, 6, 7, 8, 11, 14, 17, 18, 20, 22, 23, 24, 27, 32, 34, 35, 40, 43, 46, 47, 50, 51, 57, 58, 61, 65, 72, 73, 77, 79, 81, 84, 86, 87, 88, 92, 93, 94, 96, 97, 98, 99, 101, 102, 103, 105, 107, 114, 116, 119, 120, 123, 125, 130, 135, 137, 143, 151, 154, 155, 158, 160, 163, 164, 173, 175, 177, 179, 184, 187, 191, 193, 194, 197, 198, 200, 203, 204, 206, 209, 210, 212
Offset: 1

Views

Author

Antti Karttunen, Sep 25 2015

Keywords

Comments

Sequence A262512 sorted into ascending order.
Numbers n such that there is no other number k for which A049820(k) = A049820(n).

Links

Crossrefs

Cf. A060990, A049820, A262511, A262512.
Cf. A262509 (a subsequence).

Programs

  • Mathematica
    lim = 212; s = Table[n - DivisorSigma[0, n], {n, 2 lim + 3}]; t = Length@ Position[s, #] & /@ Range[0, lim]; Position[t[[# + 1]] & /@ Take[s, lim], 1] // Flatten (* Michael De Vlieger, Sep 29 2015, after Wesley Ivan Hurt at A049820 *)

A264988 The left edge of A263267.

Original entry on oeis.org

0, 1, 3, 5, 7, 13, 17, 19, 23, 27, 29, 31, 35, 37, 41, 43, 51, 53, 57, 59, 61, 65, 67, 71, 73, 77, 79, 143, 149, 151, 155, 157, 161, 163, 173, 177, 179, 181, 185, 191, 193, 199, 203, 209, 211, 215, 219, 223, 231, 233, 237, 239, 241, 249, 251, 263, 267, 269, 271, 277, 285, 291, 293, 299, 303, 315, 317, 321, 327, 333, 335, 337, 341, 347, 349, 357, 359, 369, 517, 531, 535, 523, 527
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2015

Keywords

Comments

The first point where the sequence is nonmonotonic is the dip from a(80) = 535 to a(81) = 523.

Links

Crossrefs

Cf. A263260, A262508, A262509.
The left edge of irregular table A263267.
Cf. A263269 (the other edge).
Differs from A261089 for the first time at n=69, where a(69) = 333, while A261089(69) = 331.

Programs

Formula

a(0) = 0; for n >= 1, a(n) = A263267(A263260(n-1)).
Other identities. For all n >= 0:
A155043(a(n)) = n.
a(A262508(n)) = A262509(n) = A263269(A262508(n)). [In case A262508 and A262509 are infinite sequences.]

A263269 The right edge of irregular table A263267.

Original entry on oeis.org

0, 2, 6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66, 70, 80, 88, 94, 102, 112, 116, 126, 124, 130, 138, 150, 148, 160, 158, 164, 184, 190, 194, 210, 214, 222, 234, 252, 246, 250, 258, 266, 272, 296, 312, 306, 320, 328, 340, 352, 364, 372, 354, 358, 368, 384, 392, 408, 402, 414, 418, 426, 434, 448, 460, 462, 470, 474, 486, 496, 510, 522, 530, 546, 558, 562, 566, 574, 582, 592, 598, 606, 630
Offset: 0

Views

Author

Antti Karttunen, Nov 29 2015

Keywords

Links

Crossrefs

Cf. A000005, A049820, A155043, A262508, A262509, A262686, A263260, A263267.
Cf. A264988 (the other edge).

Formula

a(n) = A263267(A263260(n)-1).
Other identities. For all n >= 0:
A155043(a(n)) = n.
a(A262508(n)) = A262509(n) = A264988(A262508(n)). [In case A262508 and A262509 are infinite sequences.]
Previous Showing 11-15 of 15 results.

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