cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

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Author

Labos Elemer, Dec 20 2002

Keywords

Comments

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}.

Examples

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

Crossrefs

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.

Extensions

Edited by Dean Hickerson, Dec 21 2002

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.

Original entry on oeis.org

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

Views

Author

Labos Elemer, Dec 20 2002

Keywords

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.

Examples

			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.

Extensions

Edited by Dean Hickerson, Dec 21 2002

A078871 Decimal concatenations of the 6-tuples (d1,d2,d3,d4,d5,d6) with elements in {2,4,6} for which there exists a prime p >= 7 such that the differences between the 7 consecutive primes starting with p are (d1,d2,d3,d4,d5,d6).

Original entry on oeis.org

242462, 246264, 246266, 246626, 264242, 264246, 264264, 264626, 264666, 266424, 266466, 266646, 424626, 424662, 462462, 462642, 462646, 462664, 462666, 466264, 466266, 466626, 624626, 626424, 626426, 626462, 626466, 626642, 626646, 626664, 642462, 642466, 642646, 646246, 646264, 646266, 646626, 646662, 662642, 662646, 662664, 662666, 664246, 664626, 664662, 666264, 666266, 666462
Offset: 1

Views

Author

Labos Elemer, Dec 20 2002

Keywords

Examples

			For 424662, the first 2 primes with the given differences are 37 and 25767877. For 646626, the least start prime is 6268957.

Crossrefs

The least primes corresponding to the 6-tuples are in A078874. The same primes, in increasing order, are in A078875. The similarly defined quadruples and quintuples are in A078868 and A078870. Cf. A001223, A078869.

Extensions

Edited by Dean Hickerson, Dec 21 2002
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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