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A060339 Primes that are each the sum of two, three, and four consecutive composite numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 19:34 EST 2022. Contains 350565 sequences. (Running on oeis4.)