A078872 The quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} are listed in lexicographic order; for each quintuple, this sequence lists the smallest prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5), if such a prime exists.

11, 17, 41, 29, 59, 5849, 6959, 599, 149, 3299, 7, 13, 37, 67, 1597, 19, 4639, 43, 17467, 1601, 23, 2333, 593, 6353, 1861, 31, 61, 90001, 32353, 157, 14731, 47, 587, 2671, 3307, 151, 251, 3301

Offset

1,1

Comments

Comment from N. J. A. Sloane, Dec 04 2015: (Start)

The definition of A078872 is fairly subtle.

Step 1: The 3^5 = 243 quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} are listed in lexicographic order.

Step 2: Study each quintuple in turn. Look for the smallest prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5). If there is no such prime move on to next quintuple. If there is at least one such prime, take the smallest one, add it to the sequence, and move on to the next quintuple.

Each quintuple is considered just once, so there are at most 243 terms (in fact there are only 38).

(End)

The 38 quintuples for which p exists are listed, in decimal form, in A078870.

Links

Table of n, a(n) for n=1..38.

Example

The term 67 corresponds to the quintuple (4,2,6,4,6): 67, 71, 73, 79, 83 and 89 are consecutive primes.

Crossrefs

The quintuples are in A078870. The same primes, in increasing order, are in A078873. The analogous sequences for quadruples and 6-tuples are in A078866 and A078874. Cf. A001223.

Sequence in context: A339247 A317678 A098649 * A291374 A181421 A290530

Adjacent sequences: A078869 A078870 A078871 * A078873 A078874 A078875

Keyword

nonn,fini,full

Author

Labos Elemer, Dec 20 2002

Extensions

Edited by Dean Hickerson, Dec 21 2002

Status

approved