A078873 -id:A078873 - cp's OEIS frontend

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

Labos Elemer, Dec 20 2002

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.

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

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.

Edited by Dean Hickerson, Dec 21 2002

A078875 Sorted version of A078874.

Original entry on oeis.org

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 149, 151, 251, 587, 593, 1597, 1601, 2671, 3299, 3301, 4637, 5639, 5839, 5843, 17467, 19457, 32353, 41597, 44257, 71329, 71333, 78779, 130631, 135589, 135593, 179801, 246907, 302563, 326993, 351031, 435553, 603899, 678631, 6268957

Offset: 1

Labos Elemer, Dec 20 2002

Each term is the smallest prime p >= 7 such that the differences between the 7 consecutive primes starting with p are (d1,d2,d3,d4,d5,d6), for some 6-tuple (d1,d2,d3,d4,d5,d6) with elements in {2,4,6}.

			The term 151 corresponds to the 6-tuple (6,6,4,6,6,2): 151, 157, 163, 167, 173, 179, 181 are consecutive primes.

The 6-tuples are in A078871. The same primes, in lexicographic order of the 6-tuples, are in A078874. The analogous sequences for quadruples and quintuples are in A078867 and A078873. Cf. A001223.

Edited by Dean Hickerson, Dec 21 2002

cp's OEIS Frontend

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.

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