A161667 Smallest of 5 consecutive composite numbers which sum up to prime.

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

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: A242483 A320497 A310988 * A339212 A063087 A310989

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