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 1-6 of 6 results.

A087730 Values of j for A087651 and A087732.

Original entry on oeis.org

2, 1, 2, 3, 1, 2, 5, 6, 2, 5, 1, 4, 5, 11, 6, 9, 10, 11, 13, 14, 8, 17, 11, 4, 11, 16, 19, 20, 22, 27, 16, 22, 4, 23, 24, 37, 28, 14, 23, 36, 11, 11, 15, 53, 64, 20, 75, 83, 91, 35, 72, 80, 48, 47, 2, 12, 30, 38, 54, 60, 108, 173, 13, 173, 164, 69, 121, 36, 170, 204, 285, 247, 105
Offset: 0

Views

Author

Pierre CAMI, Sep 28 2003

Keywords

Examples

			2307*2557#-1 and 2307*2557#+1 are twin primes.

Crossrefs

Cf. A002110, A087651, A086916, A087732.

Extensions

Edited by Jud McCranie and Ray Chandler, Oct 05 2003

A086916 Number of digits in terms of A087732.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 9, 9, 10, 10, 10, 10, 10, 10, 12, 13, 14, 15, 18, 20, 21, 23, 23, 23, 25, 28, 28, 29, 29, 32, 33, 35, 37, 38, 39, 41, 43, 45, 47, 50, 55, 57, 62, 62, 66, 73, 79, 92, 101, 106, 108, 115, 121, 123, 126, 131, 140, 141
Offset: 1

Views

Author

Pierre CAMI, Sep 25 2003

Keywords

Comments

Number of digits of the twin primes of the form j*P(i)# - 1 and j*P(i)# + 1 with 0 < j < P(i+1), P(i)= i rank primes, P(i)# = primorial of P(i) (A002110).

Examples

			a(23)=9 since A087732(23)=106696589 has 9 digits.
a(31)=12 since A087732(31)=103515091679 has 12 digits.

Crossrefs

Cf. A086916, A087651, A087730, A087731, A087732, A088676.

Extensions

Edited by Ray Chandler, Oct 05 2003

A088676 Values of "i" in A087732 and the index of the prime in A087731.

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 14, 15, 16, 17, 17, 17, 18, 20, 20, 20, 20, 22, 22, 23, 24, 25, 25, 26, 27, 28, 30, 31, 33, 34, 36, 36, 38, 41, 44, 49, 53, 55, 56, 59, 61, 62, 63, 65, 69, 69, 78, 85, 87, 99
Offset: 1

Views

Author

Jud McCranie, Oct 04 2003

Keywords

Examples

			17 = 3*P(2)#-1 and 19 = 3*P(2)#+1 are twin primes, so 2 is in the sequence (the 4th term).

Crossrefs

Cf. A002110, A087732.

Extensions

More terms from Ray Chandler, Oct 05 2003

A087731 Values of P for A087651.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 19, 23, 23, 23, 23, 23, 23, 23, 29, 31, 37, 37, 43, 47, 53, 59, 59, 59, 61, 71, 71, 71, 71, 79, 79, 83, 89, 97, 97, 101, 103, 107, 113, 127, 137, 139, 151, 151, 163, 179, 193, 227, 241, 257, 263, 277
Offset: 0

Views

Author

Pierre CAMI, Sep 28 2003

Keywords

Crossrefs

Cf. A000040, A002110, A086916, A087651, A087732, A088676.

Extensions

Edited by Jud McCranie, Oct 06 2003

A087651 Sequence of primorials P# (cf. A002110) such that j*P# has twin prime neighbors for some j with 0 < j < prime following P.

Original entry on oeis.org

2, 6, 6, 6, 30, 30, 30, 30, 210, 210, 2310, 2310, 2310, 2310, 30030, 30030, 30030, 30030, 30030, 30030, 510510, 510510, 9699690, 223092870, 223092870, 223092870, 223092870, 223092870, 223092870, 223092870, 6469693230, 200560490130
Offset: 0

Views

Author

Pierre CAMI, Sep 28 2003

Keywords

Comments

I think I have found a proof that the sequence is infinite.

Examples

			I have found the first 122 values of this sequence, 121 and 122 are 2557#, 2557# with j=303 and j=2307, 1087 and 1088 digits.

Crossrefs

The j values are in A087730, P values are in A087731, i values are in A088676.
Cf. A002110, A086916, A087732.
Smaller of twin primes are in A087732. Number of digits in twin primes are in A086916.

Extensions

Edited by Jud McCranie and Ray Chandler, Oct 05 2003

A257658 Primes of the form A060735(k) +- 1, where A060735 lists multiples of primorials (A002110) less than the next larger primorial.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 419, 421, 631, 839, 1049, 1051, 1259, 1471, 1889, 2099, 2309, 2311, 4621, 9239, 9241, 11549, 11551, 13859, 18481, 20789, 23099, 25409, 25411, 30029, 90089, 120121, 150151, 180179, 180181
Offset: 1

Views

Author

James M. McCanney and Robert G. Wilson v, Jul 26 2015

Keywords

Comments

After a(9), all terms are congruent to +-1 (mod 30).
More generally, for any primorial P (cf. A002110), all terms >= P-1 are congruent to +/- 1 (mod P).- This sequence is essentially the same as A087715. - M. F. Hasler, Jul 27 2015

Examples

			149 & 151 are in the sequence because they are primes +-1 from A060735(12) = 150. A term does not have to be a twin prime; those are found in A087732.

Links

Crossrefs

Cf. A060735, A087732, A002110.
Essentially the same as A087715.

Programs

  • Mathematica
    f[n_] := Range[Prime[n + 1] - 1] Times @@ Prime@ Range@ n; Select[ Union@ Flatten@ Join[ Array[f, 6] - 1, Array[f, 7, 0] + 1], PrimeQ@# &]

Formula

Primes among the numbers produced from A060735 +/- 1.
Showing 1-6 of 6 results.

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