A060339 Primes that are each the sum of two, three, and four consecutive composite numbers.

311, 337, 1009, 1103, 1511, 1777, 3671, 3889, 4271, 4657, 5737, 6841, 7561, 9649, 9769, 10223, 12239, 12889, 14759, 14831, 17401, 17569, 17783, 19009, 19031, 20903, 21529, 22369, 22751, 23279, 24049, 24889, 25057, 26423, 28871, 30671

Offset: 1

Author

Robert G. Wilson v, Mar 30 2001

Keywords

• nonn

Examples

			A(2)= 377 is equal to 168+169 = 111+112+114 = 82+84+85+86.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n=1..1000. [From _Klaus Brockhaus_, Jun 17 2009]

Crossrefs

Cf. A151744. [From Klaus Brockhaus, Jun 17 2009]

Programs

Mathematica

composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = b = c = {}; Do[ p = Sum[ composite[ n + m ], {m, 0, 1} ]; If[ PrimeQ[ p ], a = Append[ a, p ] ]; p = Sum[ composite[ n + m ], {m, 0, 2} ]; If[ PrimeQ[ p ], b = Append[ b, p ] ]; p = Sum[ composite[ n + m ], {m, 0, 3} ]; If[ PrimeQ[ p ], c = Append[ c, p ] ], {n, 1, 25000} ]; Intersection[ a, b, c ]
Module[{cmp=Select[Range[20000],CompositeQ],c2,c3,c4},c2=Total/@ Partition[ cmp,2,1];c3=Total/@Partition[cmp,3,1];c4=Total/@ Partition[ cmp,4,1];Select[ Intersection[c2,c3,c4],PrimeQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 01 2020 *)

Extensions

Definition clarified by Harvey P. Dale, Jul 01 2020