A379794 -id:A379794 - cp's OEIS frontend

A379789 Sequence Sb of the eight sequences defining the blocks of terms in A377091.

1, 3, 6, 13, 18, 25, 32, 42, 51, 62, 73, 98, 113, 128, 145, 162, 181, 201, 222, 243, 266, 290, 337, 366, 394, 419, 452, 479, 478, 516, 544, 546, 578, 613, 612, 651, 684, 721, 720, 761, 763, 804, 801, 842, 883, 926, 970, 1057, 1058, 1105, 1156, 1153, 1205, 1202, 1251, 1302, 1353, 1457, 1459, 1513, 1568, 1625, 1683, 1742, 1801

Offset: 1

N. J. A. Sloane, Jan 17 2025

nonn

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

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

Original entry on oeis.org

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 *)

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 *)

A379802 Indices k such that A377091(k) is immediately followed by A377091(k+1) = -A377091(k).

Original entry on oeis.org

2, 12, 31, 60, 90, 132, 183, 241, 307, 380, 462, 552, 677, 997, 1125, 1444, 1563, 1722, 1892, 2117, 2257, 2450, 2652, 2914, 3081, 3306, 3540, 3782, 4033, 4291, 4560, 4830, 5112, 5403, 5701, 6006, 6320, 6643, 6972, 7311, 7657, 8464, 8743, 9121, 9506, 9902, 11238, 12100, 12542, 12883, 15877, 16257, 17424, 17823, 18361, 18906, 19462

Offset: 1

N. J. A. Sloane, Jan 19 2025

nonn

			Terms 0 through 14 of A377091 are 0, 1, 2, -2, -1, 3, 4, 5, -4, -3, 6, 7, 8, -8, -7, and the pairs 2, -2 and 8, -8  correspond to a(1) = 2 and a(2) = 12.

Rémy Sigrist, Table of n, a(n) for n = 1..10000 (first 209 terms from N. J. A. Sloane)
Rémy Sigrist, C++ program

Cf. A377091, A379066, A379788-A379794, A379803, A379804, A380837.

(* A377091list is defined at A377091 *)
PositionIndex[Differences[Abs[A377091list[10000]]]][0] - 1 (* Paolo Xausa, Jan 22 2025 *)

A379803 A377091(k) for k in A379802.

Original entry on oeis.org

2, 8, -18, -32, 50, 72, -98, -128, -162, 200, 242, 288, 338, 512, -578, 722, 800, 882, 968, -1058, 1152, 1250, 1352, 1458, -1568, 1682, 1800, 1922, -2048, -2178, -2312, 2450, 2592, -2738, -2888, 3042, 3200, -3362, 3528, -3698, -3872, 4232, -4418, -4608, 4802, -5000, 5618, -6050, 6272, -6498, 7938, -8192, 8712, -8978, -9248, 9522, -9800

Offset: 1

N. J. A. Sloane, Jan 19 2025

sign

These are the values of the terms in A377091 that are immediately followed by their negatives.

			A377091(31) = -18 is immediately followed by A377091(32) = 18, so 31 is a term in A379802, and -18 is in the present sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10001 (first 209 terms from N. J. A. Sloane)
Rémy Sigrist, C++ program

Cf. A377091, A379066, A379788-A379794, A379802, A379804, A380837.

(* A377091list is defined at A377091 *)
#[[PositionIndex[Differences[Abs[#]]][0]]] & [A377091list[10000]] (* Paolo Xausa, Jan 22 2025 *)

A379804 By definition, |A379803(k)| is twice a perfect square, say 2*b(k)^2. The values of b(k) appear to be the consecutive natural numbers 1, 2, 3, ... except that the numbers in the present sequence are omitted.

Original entry on oeis.org

14, 15, 18, 45, 51, 52, 54, 58, 59, 60, 61, 62, 65, 71, 101, 102, 104, 106, 111, 114, 117, 120, 121, 122, 123, 124, 125, 126, 128, 130, 141, 161, 164, 176, 189, 203, 204, 213, 215, 229, 241, 256, 261, 262, 281, 284, 301, 306, 307, 310, 311, 312, 314, 315, 316

Offset: 1

N. J. A. Sloane, Jan 19 2025

nonn

The sequence {b(k): k >= 1} begins 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 20, ..., and as can be seen, 14, 15, and 18 are missing.

The values of b(k) are distinct.

Rémy Sigrist, Table of n, a(n) for n = 1..5000
Rémy Sigrist, C++ program

Cf. A377091, A379066, A379788-A379794, A379802, A379803.

More terms from Rémy Sigrist, Feb 09 2025

cp's OEIS Frontend

A379789 Sequence Sb of the eight sequences defining the blocks of terms in A377091.

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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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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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A379802 Indices k such that A377091(k) is immediately followed by A377091(k+1) = -A377091(k).

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A379803 A377091(k) for k in A379802.

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