A379789 -id:A379789 - cp's OEIS frontend

A380837 Sequence Sg of the eight sequences defining the blocks of terms in A377091.

4, 9, 20, 31, 42, 60, 81, 100, 121, 147, 183, 210, 241, 272, 307, 342, 400, 441, 484, 529, 576, 651, 703, 757, 813, 871, 931, 965, 1023, 1059, 1089, 1125, 1190, 1228, 1296, 1369, 1408, 1448, 1520, 1525, 1598, 1603, 1681, 1764, 1849, 1936, 2070, 2117, 2209, 2302

Offset: 1

Paolo Xausa, Feb 05 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

Apart from A379066(1) = 0, the beginning of this sequence coincides with A379066 up to a(27) = A379066(28). a(28) = 965 is the first term not present in A379066 (cf. A380838).

Paolo Xausa, Table of n, a(n) for n = 1..1000

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379792, A379793, A379794, A380838.

SequencePosition[A377091list[5000], {?Negative, ?Positive}][[All, 1]] - 1

a(n) = A379788(n+1) - 1.

A379788 Sequence Sa of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

1, 5, 10, 21, 32, 43, 61, 82, 101, 122, 148, 184, 211, 242, 273, 308, 343, 401, 442, 485, 530, 577, 652, 704, 758, 814, 872, 932, 966, 1024, 1060, 1090, 1126, 1191, 1229, 1297, 1370, 1409, 1449, 1521, 1526, 1599, 1604, 1682, 1765, 1850, 1937, 2071, 2118, 2210, 2303, 2308, 2400, 2405, 2501, 2602, 2708, 2863, 2917, 2973

Offset: 1

N. J. A. Sloane, Jan 17 2025

nonn

For this discussion let R(n) (n >= 0) denote A377091(n). Sequence A377091 starts with R(0) = 0. From then on the sequence consists of blocks of consecutive terms all with the same sign. The blocks are defined by eight sequences denoted by Sa, Sb, ..., Sh. The (2k-1)-st block (k >= 1) consists of positive terms running from R(Sa(k)) = Sb(k) to R(Sc(k)) = Sd(k). This is followed by the (2*k)-th block (k >= 1) which consists of negative terms running from R(e(k)) = -Sf(k) to R(g(k)) = -Sh(k).
The sequences Sa, ..., Sh are Sa = A379788, Sb = A379789, Sc = A379790, Sd = A379791, Se = A379792, Sf = A379793, Sg = A380837, and Sh = A379794.
The sequences are related by Sa(k) = Sg(k-1)+1 and Se(k) = Sc(k)+1, and one of each pair could be omitted from the OEIS. However, since the structure of A377091 is already sufficiently confusing, at present all eight sequences have their own entries. This also makes it simpler to define the block lengths, etc., and to use the Plot2 OEIS command.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..513 from N. J. A. Sloane).

Cf. A377091, A379789, A379790, A379791, A379792, A379793, A379794, A380837.

(* A377091list is defined at A377091 *)
SequencePosition[A377091list[5000], {?NonPositive, ?Positive}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)

A379794 Sequence Sh of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

1, 3, 12, 18, 24, 32, 39, 49, 59, 71, 98, 112, 128, 144, 162, 180, 199, 219, 241, 263, 286, 339, 363, 390, 422, 448, 482, 483, 508, 545, 543, 578, 612, 613, 645, 685, 723, 724, 760, 758, 796, 799, 839, 881, 923, 966, 1059, 1058, 1104, 1148, 1151, 1196, 1199, 1249, 1299, 1351, 1459, 1457, 1512, 1568, 1624, 1681, 1739, 1799, 1859

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..512 from N. J. A. Sloane).

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379792, A379793, A380837.

(* A377091list is defined at A377091 *)
-SequenceCases[A377091list[5000], {?Negative, ?Positive}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)

A379791 Sequence Sd of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

2, 5, 8, 12, 17, 24, 41, 50, 61, 72, 85, 97, 112, 127, 144, 161, 200, 221, 242, 265, 288, 311, 338, 362, 390, 420, 448, 481, 512, 513, 545, 543, 577, 609, 647, 686, 685, 722, 762, 760, 800, 802, 841, 882, 925, 968, 1011, 1059, 1103, 1152, 1154, 1201, 1203, 1250, 1301, 1352, 1405, 1458, 1456, 1512, 1567, 1682, 1741, 1800, 1861

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 11..513 from N. J. A. Sloane).

Cf. A377091, A379788, A379789, A379790, A379792, A379793, A379794, A380837.

(* A377091list is defined at A377091 *)
SequenceCases[A377091list[5000], {?Positive, ?Negative}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)

A379793 Sequence Sf of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

2, 4, 8, 13, 19, 25, 40, 50, 60, 72, 84, 99, 113, 129, 145, 163, 200, 220, 242, 264, 288, 314, 338, 367, 394, 421, 452, 480, 512, 511, 544, 546, 579, 616, 649, 683, 684, 722, 759, 761, 800, 798, 840, 882, 924, 968, 1014, 1057, 1106, 1152, 1150, 1200, 1198, 1250, 1300, 1352, 1404, 1458, 1460, 1513, 1569, 1682, 1740, 1800, 1860

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..513 from N. J. A. Sloane).

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379792, A379794, A380837.

(* A377091list is defined at A377091 *)
-SequenceCases[A377091list[5000], {?Positive, ?Negative}][[All, 2]] (* Paolo Xausa, Feb 05 2025 *)

A379790 Sequence Sc of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

2, 7, 12, 25, 36, 52, 73, 90, 111, 132, 160, 196, 225, 256, 289, 324, 380, 421, 462, 507, 552, 601, 677, 729, 785, 842, 900, 960, 997, 1027, 1087, 1092, 1156, 1224, 1264, 1332, 1371, 1444, 1486, 1522, 1563, 1601, 1641, 1722, 1807, 1892, 1981, 2115, 2163, 2257, 2305, 2353, 2402, 2450, 2551, 2652, 2760, 2914, 2919, 3025

Offset: 1

N. J. A. Sloane, Jan 17 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..513 from N. J. A. Sloane).

Cf. A377091, A379788, A379789, A379791, A379792, A379793, A379794, A380837.

(* A377091list is defined at A377091 *)
SequencePosition[A377091list[5000], {?Positive, ?Negative}][[All, 1]] - 1 (* Paolo Xausa, Feb 05 2025 *)

A379792 Sequence Se of the eight sequences defining the blocks of terms in A377091.

Original entry on oeis.org

3, 8, 13, 26, 37, 53, 74, 91, 112, 133, 161, 197, 226, 257, 290, 325, 381, 422, 463, 508, 553, 602, 678, 730, 786, 843, 901, 961, 998, 1028, 1088, 1093, 1157, 1225, 1265, 1333, 1372, 1445, 1487, 1523, 1564, 1602, 1642, 1723, 1808, 1893, 1982, 2116, 2164, 2258, 2306, 2354, 2403, 2451, 2552, 2653, 2761, 2915, 2920, 3026

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

See the comments in A379788 (Sequence Sa) for further information.

a(n) = A379790(n)+1.

Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..513 from N. J. A. Sloane).

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379793, A379794, A380837.

(* A377091list is defined at A377091 *)
SequencePosition[A377091list[5000], {?Positive, ?Negative}][[All, 1]] (* Paolo Xausa, Feb 05 2025 *)

A382715 The term in A377091 that immediately precedes n, or 0 if n does not appear in A377091.

Original entry on oeis.org

0, 1, -1, 3, 4, -3, 6, 7, 13, 9, 10, 11, -12, 18, 14, 15, 16, -18, 20, 21, 25, 23, 19, 28, -24, 22, 26, 27, 30, 31, 32, -32, 29, 33, 34, 35, 36, 37, 38, 39, 40, -39, 42, 43, 44, 45, 46, 47, 48, 49, -49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, -59, 62, 63, 64, 65

Offset: 1

N. J. A. Sloane, Apr 09 2025

sign

It is a strong conjecture that every integer appears in A377091, so it is unlikely there will be a second 0 term.

			A377091(9) = -3 is followed by A377091(10) = 6, so a(6) = -3.

N. J. A. Sloane, Table of n, a(n) for n = 1..10060
N. J. A. Sloane, Table of n, a(n) for n = 1..125060

Cf. A377091, A379059, A379789, A382716, A382717, A382718.

A382718 Numbers missing from A382717.

Original entry on oeis.org

4, 13, 25, 45, 53, 62, 72, 81, 84, 115, 118, 143, 145, 152, 161, 164, 170, 173, 182, 187, 192, 197, 214, 223, 228, 234, 248, 265, 272, 275, 283, 294, 302, 307, 312, 317, 319, 323, 329, 332, 341, 344, 350, 353, 355, 365, 375, 379, 382, 385, 400, 445, 455, 459, 462, 465, 480, 483, 487, 492

Offset: 1

N. J. A. Sloane, Apr 13 2025

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..7338
Rémy Sigrist, C++ program

Complement of A382717.

Cf. A377091, A382715, A382716, A379789.

A382716 a(n) = n - A382715(n).

Original entry on oeis.org

1, 1, 4, 1, 1, 9, 1, 1, -4, 1, 1, 1, 25, -4, 1, 1, 1, 36, -1, -1, -4, -1, 4, -4, 49, 4, 1, 1, -1, -1, -1, 64, 4, 1, 1, 1, 1, 1, 1, 1, 1, 81, 1, 1, 1, 1, 1, 1, 1, 1, 100, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 121, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 144, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -9, 4, 1, 1, 1, 1, 1, 1, 1, 196, -1, -4, -1, -1, 4, -9

Offset: 1

N. J. A. Sloane, Apr 09 2025

sign

Assuming that every integer appears in A377901, a(n) gives an indication of how difficult it was for the positive integer n to appear there.

(The definition of A377091 implies that |a(n)| is a square.)

N. J. A. Sloane, Table of n, a(n) for n = 1..10059

Cf. A377091, A382715.

For RECORDS, see A382717, A382718, A379789.

cp's OEIS Frontend

A380837 Sequence Sg of the eight sequences defining the blocks of terms in A377091.

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A379788 Sequence Sa of the eight sequences defining the blocks of terms in A377091.

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A379794 Sequence Sh of the eight sequences defining the blocks of terms in A377091.

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A379791 Sequence Sd of the eight sequences defining the blocks of terms in A377091.

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A379793 Sequence Sf of the eight sequences defining the blocks of terms in A377091.

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A379790 Sequence Sc of the eight sequences defining the blocks of terms in A377091.

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A379792 Sequence Se of the eight sequences defining the blocks of terms in A377091.

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A382715 The term in A377091 that immediately precedes n, or 0 if n does not appear in A377091.

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A382718 Numbers missing from A382717.

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A382716 a(n) = n - A382715(n).