A379789 -id:A379789 - cp's OEIS frontend

A382717 Square roots of record high points in A382716.

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Offset: 1

N. J. A. Sloane, Apr 13 2025

nonn

The indices of these high points are given in A379789.

			A382716 begins 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, ..., the record high points are 1, 4, 9, 25, 36, 49, ..., and taking square roots we get 1, 2, 3, 5, 6, 7, ..., which is the present sequence.

N. J. A. Sloane, Table of n, a(n) for n = 1..439

Cf. A377091, A382715, A382716, A382718 (the missing numbers), A379789.

More than the usual number of terms are shown, to help distinguish this from similar sequences.

A379795 Length of n-th block of consecutive positive terms in A377091.

Original entry on oeis.org

2, 3, 3, 5, 5, 10, 13, 9, 11, 11, 13, 13, 15, 15, 17, 17, 38, 21, 21, 23, 23, 25, 26, 26, 28, 29, 29, 29, 32, 4, 28, 3, 31, 34, 36, 36, 2, 36, 38, 2, 38, 3, 38, 41, 43, 43, 45, 45, 46, 48, 3, 46, 3, 46, 51, 51, 53, 52, 3, 53, 55, 114, 59, 59, 61, 61, 63, 63, 65, 65, 70, 133, 69, 71, 71, 73, 73, 75, 75, 154, 79, 79, 81, 164, 83, 85

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

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

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379792, A379793, A379794, A379796, A379882, A380837.

(* A377091list is defined at A377091 *)
Map[Length, SplitBy[A377091list[10000], Sign][[2 ;; -2 ;; 2]]] (* Paolo Xausa, Feb 05 2025 *)

a(n) = A379790(n) - A379788(n) + 1.

a(n) = A379882(2*n). - Rémy Sigrist, Jan 19 2025

A379796 Length of n-th block of consecutive negative terms in A377091.

Original entry on oeis.org

2, 2, 8, 6, 6, 8, 8, 10, 10, 15, 23, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 50, 26, 28, 28, 29, 31, 5, 26, 32, 2, 33, 34, 4, 32, 37, 37, 4, 34, 3, 35, 2, 40, 42, 42, 44, 89, 2, 46, 45, 2, 46, 2, 50, 50, 55, 102, 2, 53, 56, 56, 58, 58, 60, 60, 124, 64, 64, 66, 66, 68, 68, 70, 70, 144, 74, 74, 76, 76, 78, 78, 83, 159, 82, 168, 86

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..4999
Rémy Sigrist, C++ program

Cf. A377091, A379066, A379788, A379789, A379790, A379791, A379792, A379793, A379794, A379795, A379882, A380837.

(* A377091list is defined at A377091 *)
Map[Length, SplitBy[A377091list[10000], Sign][[3 ;; -2 ;; 2]]] (* Paolo Xausa, Feb 05 2025 *)

a(n) = A379066(n) - A379792(n) + 1.

a(n) = A379882(2*n + 1). - Rémy Sigrist, Jan 19 2025

A379797 In A377091, each block of consecutive terms of the same sign is followed by a jump of magnitude +-s^2 for some integer s>0 to a term of the opposite sign; sequence lists the successive values of s.

Original entry on oeis.org

2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 31, 32, 32, 32, 33, 33, 33, 33, 34, 34, 35, 35, 35, 36, 36, 37, 37, 37, 38, 38, 38, 39, 39, 39, 39, 40, 40, 40, 40, 41, 41

Offset: 1

N. J. A. Sloane, Jan 18 2025

nonn

			The initial terms of A377091 are
   0, 1, 2, -2, -1, 3, 4, 5, -4, -3, 6, 7, 8, -8, -7, -6, -5, -9, -10, -11, -12, 13, 9, 10, 11, 12, -13, -14
and the jumps we are talking about are
   __________4______4_________9______9________16__________________________________25__________________25_____
whose square roots are 2, 2, 3, 3, 4, 5, 5, ... which is the current sequence. - _N. J. A. Sloane_, Mar 30 2025

N. J. A. Sloane, Table of n, a(n) for n = 1..1024

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

See A379798 for first differences.

If n = 2*k-1, k>=1, then a(n) = sqrt{A379791(k)-A379793(k)}; if n = 2k, k>=1, then a(n) = sqrt{A379789(k+1)-A379066(k)}.

cp's OEIS Frontend

A382717 Square roots of record high points in A382716.

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A379795 Length of n-th block of consecutive positive terms in A377091.

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A379796 Length of n-th block of consecutive negative terms in A377091.

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A379797 In A377091, each block of consecutive terms of the same sign is followed by a jump of magnitude +-s^2 for some integer s>0 to a term of the opposite sign; sequence lists the successive values of s.

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