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

Author

Robert G. Wilson v, Mar 30 2001

Keywords

• nonn

Examples

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

Links

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

Programs

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 *)