A178549 a(n) is a composite number at the start of an interval of consecutive integers, ending in a prime, and non-overlapping with and at least as long as the interval addressed by a(n-1).

4, 6, 8, 12, 18, 24, 30, 38, 48, 60, 72, 84, 98, 114, 132, 150, 168, 192, 224, 258, 294, 332, 374, 420, 468, 522, 578, 642, 710, 788, 878, 968, 1062, 1164, 1278, 1400, 1524, 1658, 1802, 1950, 2100, 2252, 2412, 2580, 2750, 2928, 3110, 3300, 3492, 3692, 3908

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 29 2010

Keywords

• nonn

Comments

Non-overlapping intervals of the integers of nondecreasing length, starting with a composite number and ending with a prime number, define an intermediate table (as below), the first column of which defines the sequence.

4, 5

6, 7

8, 9, 10, 11

12, 13, 14, 15, 16, 17

18, 19, 20, 21, 22, 23

24, 25, 26, 27, 28, 29

30, 31, 32, 33, 34, 35, 36, 37

38, 39, 40, 41, 42, 43, 44, 45, 46, 47

48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59

60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Crossrefs

Cf. A070865, A178547.

Programs

Mathematica

PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; d=0;p=2;lst={}; Do[d=PrimeNext[p+d]-p;p=p+=d;d--;AppendTo[lst,p+1],{n,0,5!}];lst

Formula

a(n) = 1 + A070866(n+1). - R. J. Mathar, Jun 07 2010

Extensions

Definition rephrased by R. J. Mathar, Jun 07 2010