A141275 -id:A141275 - cp's OEIS frontend

A141274 Composite numbers k such that k+1 is prime and the index in the composites is also prime.

12, 28, 36, 60, 100, 130, 138, 150, 172, 180, 198, 222, 270, 292, 348, 396, 420, 432, 456, 520, 540, 568, 612, 618, 640, 682, 732, 768, 786, 820, 838, 880, 928, 996, 1032, 1060, 1068, 1090, 1096, 1212, 1222, 1276, 1300, 1306, 1320, 1372, 1428, 1486, 1548

Offset: 1

Enoch Haga, Jun 21 2008

Suggested by Carlos Rivera's Puzzle 449.

			a(1) = 12 because 12+1 = 13, prime and the index of 12 is 5, so both the composite 12+1 and the index are prime.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Carlos Rivera, Puzzle 449. Count N composites after p, The Prime Puzzles & Problems Connection.

Cf. A141275.

Select[Range[4,1548],!PrimeQ[#]&&PrimeQ[#+1]&&PrimeQ[#-PrimePi[#]-2]&] (* James C. McMahon, Jul 19 2025 *)

from sympy import compositepi, isprime
def ok(n):
    return not isprime(n) and isprime(n+1) and isprime(compositepi(n)-1)
print([k for k in range(1549) if ok(k)]) # Michael S. Branicky, Dec 28 2021

Compute the composite numbers beginning with 4. At 4 the composite index is zero, at 6 it is 1, at 8 it is 2, ... and at 12 it is 5, etc.

Edited by N. J. A. Sloane, Jun 21 2008

A141278 Clusters of consecutive composites in A141089.

Original entry on oeis.org

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

cp's OEIS Frontend

A141274 Composite numbers k such that k+1 is prime and the index in the composites is also prime.

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