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

1,1

Comments

Suggested by Carlos Rivera's Puzzle 449, The Prime Puzzles & Problems Connection

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

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.

Example

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.

Prog

(Python)
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

Crossrefs

Cf. A141275.

Sequence in context: A253534 A255136 A087252 * A224613 A134618 A108405

Adjacent sequences: A141271 A141272 A141273 * A141275 A141276 A141277

Keyword

easy,nonn

Author

Enoch Haga, Jun 21 2008

Extensions

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

Status

approved