A053767 -id:A053767 - cp's OEIS frontend

A141278 Clusters of consecutive composites in A141089.

25, 26, 48, 49, 114, 115, 123, 124, 212, 213, 287, 288, 332, 333, 342, 343, 398, 399, 415, 416, 440, 441, 446, 447, 470, 471, 488, 489, 510, 511, 512, 548, 549, 553, 554, 603, 604, 638, 639, 640, 648, 649, 675, 676, 771, 772, 785, 786, 818, 819, 836, 837

Offset: 1

Enoch Haga, Jun 21 2008

A141089 contains composites A002808(k) such that the partial sum A053767(k) divides the partial product A036691(k). The sequence contains the subsequences of A141089 that contain two or more consecutive integers.

			The first pair of consecutive integers is (25,26) in A141089(6,7), the second (48,49) in A141089(9,10).
Triples of consecutive integers in A141089 are (510,511,512), (638,639,640), (889,890,891), (912,913,914), quadruples are (987,988,989,990), etc, all members included here.

Cf. A141089 A141090 A141091 A141092 A141274 A141275.

Numbers A141089(i) such that either 1+A141089(i) = A141089(i+1) or A141089(i)-1 = A141089(i-1) or both.

Edited by R. J. Mathar, Jul 08 2008

A255383 Compositorial mod sum-of-composites.

Original entry on oeis.org

0, 4, 12, 0, 1, 41, 0, 72, 2, 0, 48, 126, 0, 20, 0, 0, 90, 95, 115, 4, 0, 140, 161, 90, 261, 138, 208, 512, 72, 420, 51, 0, 0, 924, 899, 29, 893, 72, 840, 727, 129, 1185, 194, 732, 1080, 1612, 566, 175, 1352, 1192, 1204, 1360, 428, 957, 2170, 0, 0, 513, 2240

Offset: 1

Walter Carlini, May 14 2015

			For n = 5, a(5) = (4*6*8*9*10) mod (4+6+8+9+10) = 17280 mod 37 = 1.

Cf. A002808, A036691, A053767, A255217.

comp=Select[Range[2,83],!PrimeQ[#]&];Mod[Rest[FoldList[Times,1,comp]],Accumulate[comp]] (* Ivan N. Ianakiev, May 22 2015 *)

a(n) = A036691(n) mod A053767(n).

More terms from Alois P. Heinz, May 21 2015

cp's OEIS Frontend

A141278 Clusters of consecutive composites in A141089.

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