A232221 -id:A232221 - cp's OEIS frontend

A232359 Positions of peak values in A232221.

425, 439, 561, 565, 633, 639, 678, 857, 883, 889, 1148, 2641, 3283, 3590, 3619, 3626, 3628, 4424, 4904, 4917, 4979, 4985, 5061, 7631, 7651, 7676, 7771, 7782, 7801, 7805, 8960, 9340, 9362, 9371, 9414, 9422, 9424, 9428, 9454, 9459, 9773, 10421, 10425, 10450

Offset: 1

Reinhard Zumkeller, Nov 24 2013

nonn

max{A232221(a(n)-1),A232221(a(n)+1)} < A232221(a(n)) = A232361(n).

			Cf. A232361.

Reinhard Zumkeller, Table of n, a(n) for n = 1..890

a232359 n = a232359_list !! (n-1)
(a232359_list, a232361_list) = unzip $
   f 2 (tail a232221_list) $ zipWith (-) (tail a232221_list) a232221_list
   where f x (y:ys) (u:ws@(v:_))
           | u > 0 && v < 0 = (x, y) : f (x + 1) ys ws
           | otherwise      = f (x + 1) ys ws

A232361 Peak values in A232221.

Original entry on oeis.org

590868, 586496, 392956, 392612, 369532, 371872, 348760, 92820, 98000, 97424, 268428, 7855172, 11351516, 12763068, 12778820, 12778872, 12778940, 14485860, 16971756, 16976632, 17062548, 17065428, 16934020, 33084456, 33100460, 33116544, 32916668, 32921404

Offset: 1

Reinhard Zumkeller, Nov 24 2013

sign

max{A232221(A232359(n)-1),A232221(A232359(n)+1)} < a(n).

First entry < 0: a(77) = -279411084.

			n = 17: A232359(17) = 3628, a(17) = 12778940:
A232221(3628) = 12778940, whereas A232221(3628-1) = 12778756 and A232221(3628+1) = 12778920 are both less than a(17), with altitude differences 184 and 20. Therefore a(17) is the altitude of a peak in A232221. It can be identified in oeis.org/A232221/graph as top of a foothill.
n = 461: A232359(461) = 373250, a(461) = -2419822248:
A232221(373250) = -2419822248, whereas A232221(373250-1) = -2419823140 and A232221(373250+1) = -2419823192 are both less than a(461), with altitude differences 892 and 944. Therefore a(461) is the altitude of a peak in A232221. It can be identified in Hans Havermann's third plot (< 1.5 million) as the below-axis peak under the 4 of 400000.

Reinhard Zumkeller, Table of n, a(n) for n = 1..890

a232361 n = a232361_list !! (n-1)  -- a232361_list is defined in A232359.

a(n) = A232221(A232359(n)).

A233973 a(n) = A232221(n)/4.

Original entry on oeis.org

0, 0, 1, 5, 9, 13, 32, 54, 82, 116, 159, 199, 227, 273, 331, 380, 429, 487, 536, 609, 679, 743, 816, 895, 953, 1008, 1042, 1067, 1104, 1180, 1253, 1332, 1429, 1532, 1626, 1675, 1733, 1812, 1921, 2045, 2169, 2317, 2420, 2535, 2656, 2756, 2850, 2953

Offset: 1

Omar E. Pol, Dec 18 2013

nonn

Cf. A001358, A077065, A077068, A232221.

a(n) = (Sum_{i=1..n} (A077068(i)-A077065(i)))/4.

A232342 A077068(n) minus A077065(n).

Original entry on oeis.org

0, 0, 4, 16, 16, 16, 76, 88, 112, 136, 172, 160, 112, 184, 232, 196, 196, 232, 196, 292, 280, 256, 292, 316, 232, 220, 136, 100, 148, 304, 292, 316, 388, 412, 376, 196, 232, 316, 436, 496, 496, 592, 412, 460, 484, 400, 376, 412, 556, 736, 1000, 940, 1012

Offset: 1

Reinhard Zumkeller, Dec 16 2013

sign

All terms are multiples of 4, cf. A008586;
a(n) = A077068(n) - A077065(n).
First term < 0: a(426) = -104.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A232221 (partial sums).

a232342 n = a232342_list !! (n-1)
a232342_list = zipWith (-) a077068_list a077065_list

cp's OEIS Frontend

A232359 Positions of peak values in A232221.

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A232361 Peak values in A232221.

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Haskell

Formula

A233973 a(n) = A232221(n)/4.

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Formula

A232342 A077068(n) minus A077065(n).

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Haskell