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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

Table of n, a(n) for n=1..52.

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

Cf. A060329, A060330, A161666

Sequence in context: A310987 A242483 A310988 * A063087 A310989 A310990

Adjacent sequences:  A161664 A161665 A161666 * A161668 A161669 A161670

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jun 15 2009

EXTENSIONS

Comment from Charles R Greathouse IV, Nov 11 2009

STATUS

approved

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Last modified September 22 08:23 EDT 2018. Contains 315270 sequences. (Running on oeis4.)