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 1-9 of 9 results.

A266512 Smallest prime starting a (nonsingular) symmetric n-tuplet of the shortest span (=A266511(n)).

Original entry on oeis.org

2, 3, 47, 5, 18713, 7, 12003179, 17, 1480028129, 13, 1542186111157, 41280160361347, 660287401247633, 10421030292115097, 3112462738414697093, 996689250471604163, 258406392900394343851, 824871967574850703732309, 9425346484752129657862217, 824871967574850703732303
Offset: 1

Views

Author

Max Alekseyev, Dec 30 2015

Keywords

Comments

A similar sequence that allows singular symmetric n-tuples is given in A266583.
a(1)-a(10) from Natalia Makarova
a(11)-a(14), a(16) from Dmitry Petukhov
a(15), a(17) from Jaroslaw Wroblewski

Links

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266583, A266584.

Formula

a(n) = A000040(A266584(n)).

Extensions

a(18) from Jaroslaw Wroblewski
a(20) from Natalia Makarova and Jaroslaw Wroblewski
a(19) from Dmitry Petukhov, Anton Nikonov and Ruslan Vikulov, Jan 24 2025

A266584 Smallest m such that prime(m) starts a (nonsingular) symmetric n-tuplet of consecutive primes of the smallest span (=A266511(n)).

Original entry on oeis.org

1, 2, 15, 3, 2136, 4, 788244, 7, 73780392, 6, 57067140928, 1361665032086, 19953429852608, 290660101635794, 74896929428416952, 24660071077535201, 5620182896687887031
Offset: 1

Views

Author

Max Alekseyev, Jan 01 2016

Keywords

Comments

See A266583 for further comments and the relation to A266585.
A000040(a(n)+n-1) - A000040(a(n)) = A266511(n).

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266512, A261323, A261324, A266583, A266585.

Formula

a(n) = A000720(A266512(n)).

Extensions

More terms from Max Alekseyev, Jul 24 2019

A335044 Primes starting 14-tuples of consecutive primes that have symmetrical gaps about their mean and form 7 pairs of twin primes.

Original entry on oeis.org

1855418882807417, 2485390773085247, 4038284355308309, 14953912258447817, 16152884167551797, 20149877129714999, 23535061700758967, 24067519779525107, 25892136591156917, 28681238268465371, 29359755788438639, 38364690814563809, 52367733685120277
Offset: 1

Views

Author

Tomáš Brada, Jun 05 2020

Keywords

Examples

			a(1) = A274792(7) = 1855418882807417 starts a 14-tuple of consecutive primes: 1855418882807417+s for s in {0 2 12 14 30 32 72 74 114 116 132 134 144 146} that are symmetric about 1855418882807417+73 and form 7 pairs of twin primes.

Links

Crossrefs

Cf. A330278, A274792, A055380, A055381, A055382, A081235, A266511, A266512.

A266583 Smallest prime starting a symmetric n-tuple of consecutive primes of the smallest span (=A266676(n)).

Original entry on oeis.org

2, 2, 3, 5, 18713, 5, 12003179, 17, 1480028129, 13, 1542186111157, 41280160361347, 660287401247633, 10421030292115097, 3112462738414697093, 996689250471604163, 258406392900394343851, 824871967574850703732309, 9425346484752129657862217, 824871967574850703732303
Offset: 1

Views

Author

Max Alekseyev, Jan 01 2016

Keywords

Comments

An n-tuple (p(1),...,p(n)) is symmetric if p(k)+p(n+1-k) is the same for all k=1,2,...,n (cf. A175309).
In contrast to A266512, n-tuples here may be singular and give the complete set of residues modulo some prime. For example, for n=3 we have the symmetric 3-tuple: (3,5,7) = (3,3+2,3+4), but there are no other symmetric 3-tuples of the form (p,p+2,p+4), since one of its elements would be divisible by 3.
For any n, a(n) <= n or a(n) = A266512(n).

Links

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266512, A261324.

Formula

a(n) = A000040(A266585(n)).

Extensions

a(18)-a(20) added by Dmitry Petukhov, Feb 15 2025

A335394 Primes starting 16-tuples of consecutive primes that have symmetrical gaps about their mean and form 8 pairs of twin primes.

Original entry on oeis.org

2640138520272677, 119890755200639999, 156961225134536189, 193609877401516181, 215315384130681929, 404072710417411769, 517426190585100089, 519460320704755811
Offset: 1

Views

Author

Tomáš Brada, Natalia Makarova Jun 05 2020

Keywords

Examples

			a(1) = A274792(8) = 2640138520272677 starts a 16-tuple of consecutive primes: 2640138520272677+s for s in {0, 2, 12, 14, 30, 32, 54, 56, 90, 92, 114, 116, 132, 134, 144, 146} that are symmetric about 2640138520272677+73 and form 8 pairs of twin primes.

Crossrefs

Cf. A330278, A274792, A055380, A055381, A055382, A081235, A266511, A266512.

A266585 Smallest m such that prime(m) starts a symmetric n-tuple of consecutive primes of the smallest span (=A266676(n)).

Original entry on oeis.org

1, 1, 2, 3, 2136, 3, 788244, 7, 73780392, 6, 57067140928, 1361665032086, 19953429852608, 290660101635794, 74896929428416952, 24660071077535201, 5620182896687887031
Offset: 1

Views

Author

Max Alekseyev, Jan 01 2016

Keywords

Comments

See A266583 for further comments and the relation to A266584.
A000040(a(n)+n-1) - A000040(a(n)) = A266676(n).

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266512, A261323, A261324, A266583, A266584.

Formula

a(n) = A000720(A266583(n)).

Extensions

More terms from Max Alekseyev, Jul 24 2019

A266676 Smallest span (difference between the start and end) of a symmetric n-tuple of consecutive primes.

Original entry on oeis.org

0, 1, 4, 8, 36, 14, 60, 26, 84, 34, 132, 46, 168, 56, 180, 74, 240, 82
Offset: 1

Views

Author

Max Alekseyev, Jan 02 2016

Keywords

Comments

An n-tuple (p(1),...,p(n)) is symmetric if p(k)+p(n+1-k) is the same for all k=1,2,...,n (cf. A175309).
In contrast to A266511, n-tuples here may be singular and give the complete set of residues modulo some prime. For example, for n=3 we have the symmetric 3-tuple: (3,5,7) = (3,3+2,3+4) of span a(3)=4, but there are no other symmetric 3-tuples of the form (p,p+2,p+4), since one of its elements would be divisible by 3.
a(n) <= A266511(n).

Crossrefs

The smallest starting primes and their indices of the corresponding tuples are given in A266583 and A266585.
Cf. A055380, A065688, A175309, A266511, A266512, A261324.

A330278 Primes starting 12-tuples of consecutive primes that have symmetrical gaps about their mean and form 6 pairs of twin primes.

Original entry on oeis.org

17479880417, 158074620437, 1071796554401, 1087779101699, 1153782400787, 1628444511389, 2066102452949, 2083857437327, 2561560206377, 3731086236287, 3751571181929, 4158362831639, 4878193583477, 5008751356547, 5378606656847, 5531533689527, 7020090738707, 7036216236989
Offset: 1

Views

Author

Max Alekseyev, Dec 08 2019

Keywords

Examples

			a(1) = A274792(6) = 17479880417 starts a 12-tuple of consecutive primes: 17479880417+s for s in {0, 2, 24, 26, 30, 32, 54, 56, 60, 62, 84, 86} that are symmetric about 17479880417+43 and form 6 pairs of twin primes.

Links

Crossrefs

Cf. A055380, A055381, A055382, A081235, A266511, A266512.

Extensions

a(2)-a(6) from Franz-Xaver Harvanek
More terms from Giovanni Resta, Dec 10 2019

A336966 Primes starting 10-tuples of consecutive primes that have symmetrical gaps about their mean and form 5 pairs of twin primes.

Original entry on oeis.org

3031329797, 5188151387, 14168924459, 14768184029, 18028534367, 26697800819, 26919220961, 29205326387, 32544026699, 39713433671, 45898528799, 48263504459, 50791655009, 66419473031, 71525244611, 80179195037, 83700877199, 86767580069, 97660776137, 108116163479
Offset: 1

Views

Author

Tomáš Brada, Aug 09 2020

Keywords

Examples

			a(1) = A274792(5) = 3031329797 starts a 10-tuple of consecutive primes: 3031329797+s for s in {0, 2, 12, 14, 42, 44, 72, 74, 84, 86} that are symmetric about 3031329797+43 and form 5 pairs of twin primes.

Crossrefs

Cf. A055380, A055381, A055382, A081235, A266511, A266512, A335044, A335394, A336966, A336968.
Showing 1-9 of 9 results.

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