A166039 -id:A166039 - cp's OEIS frontend

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

Robert G. Wilson v, Mar 30 2001

nonn

"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

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

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.

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

A257392 Number of ways of representing n as the sum of one or more consecutive nonprime numbers (A018252).

Original entry on oeis.org

1, 2, 0, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 3, 3, 1, 1, 2, 1, 2, 2, 1, 2, 1, 4, 2, 1, 2, 1, 1, 1, 4, 2, 0, 1, 4, 3, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 4, 3, 2, 1, 3, 2, 3, 1, 2, 1, 0, 3, 4, 2, 2, 3, 3, 1, 3, 2, 1, 2, 3, 2, 2, 1, 1, 4, 2, 2, 1, 4, 5

Offset: 1

Juri-Stepan Gerasimov, Apr 21 2015

nonn

			a(2) = 2 because n = 2 itself is already a nonprime number (sum of 1 term), and 1 can in addition be written as A018252(1) + A018252(2), a sum of 2 consecutive nonprime numbers.

Cf. A051349, A053767, A018252, A166037, A166039, A242667, A257393.

cp's OEIS Frontend

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

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