A060328 Primes which are the sum of three consecutive composite numbers.

23, 31, 41, 59, 67, 71, 109, 113, 131, 139, 157, 199, 211, 239, 251, 269, 293, 311, 337, 379, 383, 409, 419, 487, 491, 499, 503, 521, 571, 599, 631, 701, 751, 769, 773, 787, 829, 877, 881, 919, 941, 953, 991, 1009, 1013, 1039, 1049, 1061, 1103, 1117, 1151

Offset

1,1

Comments

"Consecutive" necessarily means consecutive in the list of composite numbers as opposed to consecutive in the integers, as the sum of any 3 consecutive integers is a multiple of 3. - Peter Munn, Aug 20 2023

Links

Table of n, a(n) for n=1..51.

Example

a(3) = 41 is equal to 12+14+15.

Mathematica

composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); b = {}; Do[ p = composite[ n ] + composite[ n + 1 ] + composite[ n + 2 ]; If[ PrimeQ[ p ], b = Append[ b, p ] ], {n, 1, 1000} ]; b

Crossrefs

Primes that are the sum of other numbers of consecutive composite numbers: A060254 (2), A060329 (4), A060330 (5), A060331 (6), A060332 (7), A060333 (8). See also A037174.

Cf. A034962.

Complement within A166039\{5, 11} of A151741.

Sequence in context: A169640 A026051 A141818 * A034962 A133659 A309354

Adjacent sequences: A060325 A060326 A060327 * A060329 A060330 A060331

Keyword

nonn

Author

Robert G. Wilson v, Mar 30 2001

Status

approved