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.

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A095962 If p(x) is the x-th prime, then the n-th set of 3 consecutive sexy prime pairs starts at p(a(n)).

Original entry on oeis.org

54, 103, 271, 345, 347, 354, 464, 504, 682, 709, 767, 787, 821, 823, 825, 827, 1086, 1157, 1319, 1557, 1607, 1722, 1724, 1842, 2009, 2207, 2209, 2771, 2773, 2876, 2917, 3034, 3164, 3166, 3253, 3339, 3470, 3504, 3819, 3921, 4272, 4350, 4352, 4751, 4753
Offset: 1

Views

Author

Ray G. Opao, Jul 15 2004

Keywords

Examples

			a(2)=103. p(103)=563 and p(104)=569, the first sexy prime pair. p(105)=571 and p(106)=577, the second sexy prime pair. p(107)=587 and p(108)=593, the third sexy prime pair.

Crossrefs

Cf. A023201, A046117.

A095963 If p(x) is the x-th prime, then the n-th set of 4 consecutive sexy prime pairs starts at p(a(n)).

Original entry on oeis.org

345, 821, 823, 825, 1722, 2207, 2771, 3164, 4350, 4751, 6201, 7616, 7686, 8141, 10138, 10140, 10827, 10829, 12217, 12219, 12915, 14128, 14130, 16386, 16746, 21417, 21594, 21724, 21726, 21777, 21788, 26561, 28594, 29519, 29662, 30573
Offset: 1

Views

Author

Ray G. Opao, Jul 15 2004

Keywords

Examples

			a(1)=345. p(345)=2333 and p(346)=2339, the first sexy prime pair. p(347)=2341 and p(348)=2347, the second sexy prime pair. p(349)=2351 and p(350)=2357, the third sexy prime pair. p(351)=2371 and p(352)=2377, the fourth sexy prime pair.

Crossrefs

Cf. A023201, A046117.

A095964 If p(x) is the x-th prime, then the n-th set of 5 consecutive sexy prime pairs starts at p(a(n)).

Original entry on oeis.org

821, 823, 10138, 10827, 12217, 14128, 21724, 30929, 48132, 63375, 67244, 95411, 118666, 127721, 157547, 157549, 214245, 243947, 261071, 261996, 264314, 281625, 284778, 322576, 340791, 340793, 344154, 362020, 367638, 393331, 405109, 405111
Offset: 1

Views

Author

Ray G. Opao, Jul 15 2004

Keywords

Examples

			a(3)=10138. p(10138)=106357 and p(10139)=106363, the first sexy prime pair. p(10140)=106367 and p(10141)=106373, the second sexy prime pair. p(10142)=106391 and p(10143)=106397, the third sexy prime pair. p(10144)=106411 and p(10145)=106417, the fourth sexy prime pair. p(10146)=106427 and p(10147)=106433, the fifth sexy prime pair.

Crossrefs

Cf. A023201, A046117.

A095965 If p(x) is the x-th prime, then the n-th set of 6 consecutive sexy prime pairs starts at p(a(n)).

Original entry on oeis.org

821, 157547, 340791, 405109, 405111, 409732, 419101
Offset: 1

Views

Author

Ray G. Opao, Jul 15 2004

Keywords

Comments

a(8)>500000

Examples

			a(2)=157547. p(157547)=2125451 and p(157548)=2125457, the first sexy prime pair. p(157549)=2125463 and p(157550)=2125469, the second sexy prime pair. p(157551)=2125471 and p(157552)=2125477, the third sexy prime pair. p(157553)=2125517 and p(157554)=2125523, the fourth sexy prime pair. p(157555)=2125531 and p(157556)=2125537, the fifth sexy prime pair. p(157557)=2125553 and p(157558)=2125559, the sixth sexy prime pair.

Crossrefs

Cf. A023201, A046117.

A104043 Primes p equal to the sum of two successive sexy primes + 1 such that p + 6 is also prime.

Original entry on oeis.org

17, 41, 53, 101, 173, 353, 461, 1013, 1181, 1301, 1361, 1901, 2441, 4001, 4133, 4673, 4793, 5381, 5393, 5801, 6653, 10601, 11801, 12101, 12641, 12653, 15641, 15761, 16481, 19073, 21221, 23561, 23813, 23873, 25301, 25793, 25841, 25913, 26921
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 31 2005

Keywords

Crossrefs

Cf. A023201, A046117.

Formula

A104228 INTERSECT A023201. [From R. J. Mathar, Nov 26 2008]

Extensions

Removed 31 and extended by R. J. Mathar, Nov 26 2008

A104047 Primes p equal to the sum of two successive sexy primes - 1 such that p - 6 is also prime.

Original entry on oeis.org

19, 67, 79, 199, 547, 619, 739, 1459, 1759, 3319, 3739, 4027, 4567, 5107, 5419, 6367, 7219, 8719, 9187, 9907, 10459, 10867, 11119, 12547, 13099, 14827, 15739, 16927, 17047, 18307, 21319, 25939, 27259, 27367, 31327, 33967, 37579, 38839, 38959
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 31 2005

Keywords

Crossrefs

Cf. A023201, A046117.

Programs

  • Mathematica
    Select[2#+5&/@Select[Prime[Range[4200]],PrimeQ[#+6]&],And@@PrimeQ[ {#,#-6}]&] (* Harvey P. Dale, Feb 28 2012 *)

Formula

A104227 INTERSECT A046117. [From R. J. Mathar, Nov 26 2008]

Extensions

23 and 29 removed, extended by R. J. Mathar, Nov 26 2008

A128539 Lucky numbers with size of gaps equal to 6 (lower terms).

Original entry on oeis.org

1, 3, 7, 9, 15, 25, 31, 37, 43, 63, 67, 69, 73, 87, 93, 99, 105, 127, 129, 135, 163, 189, 195, 205, 231, 235, 261, 267, 283, 297, 321, 361, 385, 393, 409, 415, 421, 427, 477, 483, 489, 511, 529, 535, 553, 577, 613, 615, 639, 645, 673, 679, 693, 717, 723, 729
Offset: 1

Views

Author

Jonathan Vos Post, May 08 2007

Keywords

Comments

This is to (A031886) Lucky numbers with size of gaps equal to 4 (lower terms) as (A023201) smaller member of sexy prime pairs are to (A023200) smaller member p of cousin prime pairs.
Supersequence of A031888. [From R. J. Mathar, Oct 22 2010]

Crossrefs

Cf. A000959, A023200, A023201, A031886.

Formula

{L in A000959 such that L+6 in A000959}.

Extensions

More terms from R. J. Mathar, Oct 22 2010

A190797 For primes p and q=p+6 create primitive Pythagorean triangles with sides (q^2 - p^2)/2, (p^2 + q^2)/2, and p*q. If the two remainders of the middle and longest side modulo the shortest side are both prime, then p is in the sequence.

Original entry on oeis.org

11, 23, 41, 83, 107, 167, 191, 263, 307, 347, 367, 461, 641, 653, 877, 881, 1103, 1187, 1367, 2081, 2393, 2677, 3607, 4283, 4357, 4967, 5081, 5231, 5387, 5471, 5651, 6037, 6197, 6311, 6353, 6857, 7823, 8117, 8693, 8747, 9221, 9743, 9851, 9923
Offset: 1

Views

Author

J. M. Bergot, May 20 2011

Keywords

Comments

The short side is 6p+18, the middle side p^2+6p, the long side 6p+18+p^2.
The first few values have more terms == 3 (mod 4) than 1 (mod 4), but this does not appear to be the case for later terms. - Franklin T. Adams-Watters, May 22 2011

Examples

			For p=41 and q=47, the sides are (47^2 - 41^20)/2=264, 41*47=1927 and (41^2 + 43^2)/2=1945; divide 1927 and 1945 through 264 to get remainders 79 and 97.  Since both are primes, p=41 is in the sequence.

Crossrefs

Cf. A023201.

Programs

  • PARI
    forprime(p=5,10000,if(isprime(q=p+6),x=(q^2-p^2)/2;if(isprime(((q^2+p^2)/2)%x)&isprime(p*q%x),print1(p", "))))

Formula

If p=6k+5, then the remainders are 7 + 12*k and 25 + 12*k.
If p=6k+1, then the remainders are 7 + 24*k and 25 + 24*k.

Extensions

Corrected and extended by Franklin T. Adams-Watters, May 22 2011

A208123 Lengths of sequences of sexy primes in arithmetic progression with a common difference of six.

Original entry on oeis.org

5, 3, 3, 4, 4, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 4, 3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3
Offset: 1

Views

Author

Eliot Ball, Mar 26 2012

Keywords

Comments

No numbers in the sequence are greater than 5, and 5 only appears once, at the start.

Examples

			The first four sequences of sexy primes in arithmetic progression with common difference of six (they are 'chained together') are (5, 11, 17, 23, 29), (7, 13, 19), (31, 37, 43), (41, 47, 53, 59).

Crossrefs

Cf. A023201, A046117.

A239007 Difference between the smallest 10^n-digit member of a sexy prime pair and 10^(10^n - 1).

Original entry on oeis.org

4, 87, 34951, 73203, 475341523
Offset: 0

Views

Author

Arkadiusz Wesolowski, Mar 08 2014

Keywords

Links

  • G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 10000...34951 (100-digits)
  • Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- _N. J. A. Sloane_, Mar 07 2021]

Crossrefs

Cf. A023201.

Programs

  • Mathematica
    lst = {}; Do[s = 10^(10^n - 1); n = NextPrime[s]; While[! PrimeQ[n + 6], n = NextPrime[n]]; AppendTo[lst, n - s], {n, 0, 2}]; lst
Previous Showing 101-110 of 119 results. Next

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

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