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A161667 Smallest of 5 consecutive composite numbers which sum up to prime. 0
4, 8, 10, 14, 16, 28, 56, 58, 68, 70, 98, 106, 134, 146, 148, 178, 188, 190, 194, 196, 236, 308, 310, 344, 346, 428, 520, 566, 568, 614, 638, 640, 658, 808, 824, 854, 856, 1018, 1028, 1030, 1058, 1226, 1276, 1318, 1448, 1480, 1484, 1616, 1784, 1876, 1946, 2024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are at most 5n/log n members of this sequence up to n, since at least one of a(n), a(n) + 1, ..., a(n) + 4 is prime (else their sum is divisible by 5).
LINKS
EXAMPLE
4+6+8+9+10=37,.. p=37,53,67,83,97,157,..(A060330)
MATHEMATICA
CompositeNext[n_]:=Module[{k=n+1}, While[PrimeQ[k], k++ ]; k]; lst={}; Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]]+CompositeNext[CompositeNext[CompositeNext[n]]]+CompositeNext[CompositeNext[CompositeNext[CompositeNext[n]]]]; If[ !PrimeQ[n]&&PrimeQ[p], AppendTo[lst, n]], {n, 2, 5*6!}]; lst
Transpose[Select[Partition[Select[Range[2100], CompositeQ], 5, 1], PrimeQ[ Total[ #]]&]][[1]] (* Harvey P. Dale, Aug 14 2014 *)
CROSSREFS
Sequence in context: A242483 A320497 A310988 * A339212 A063087 A310989
KEYWORD
nonn
AUTHOR
EXTENSIONS
Comment from Charles R Greathouse IV, Nov 11 2009
STATUS
approved

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Last modified May 27 02:37 EDT 2024. Contains 372847 sequences. (Running on oeis4.)