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

1,1

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A281568 A084876 A190567 * A046016 A142005 A059225

Adjacent sequences: A060336 A060337 A060338 * A060340 A060341 A060342

Keyword

nonn

Author

Robert G. Wilson v, Mar 30 2001

Extensions

Definition clarified by Harvey P. Dale, Jul 01 2020

Status

approved