A060327 Primes the sum of both two and three consecutive composite numbers.

31, 41, 67, 71, 109, 113, 131, 139, 199, 211, 239, 251, 269, 293, 311, 337, 379, 409, 419, 487, 491, 499, 521, 571, 599, 631, 701, 751, 769, 773, 787, 829, 881, 919, 941, 953, 991, 1009, 1013, 1039, 1049, 1061, 1103, 1117, 1151, 1193, 1229, 1291, 1301

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(2) = 41 which is equal to 20+21 and 12+14+15.

Mathematica

composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = {}; Do[ p = composite[ n ] + composite[ n + 1 ]; If[ PrimeQ[ p ], a = Append[ a, p ] ], {n, 1, 1000} ]; b = {}; Do[ p = composite[ n ] + composite[ n + 1 ] + composite[ n + 2 ]; If[ PrimeQ[ p ], b = Append[ b, p ] ], {n, 1, 1000} ]; Intersection[ a, b ]
Module[{cmps=Select[Range[700], CompositeQ], c2, c3}, c2=Total/@Partition[cmps, 2, 1]; c3=Total/@Partition[cmps, 3, 1]; Select[Intersection[c2, c3], PrimeQ]] (* Harvey P. Dale, Nov 12 2022 *)

Crossrefs

Sequence in context: A089721 A089442 A243704 * A202286 A285805 A141180

Adjacent sequences: A060324 A060325 A060326 * A060328 A060329 A060330

Keyword

nonn

Author

Robert G. Wilson v, Mar 30 2001

Status

approved