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 1-10 of 15 results. Next

A125830 Primes for which the level is equal to 1 in A117563.

Original entry on oeis.org

5, 13, 23, 31, 47, 53, 73, 157, 173, 211, 233, 257, 263, 353, 373, 563, 593, 607, 619, 647, 653, 733, 947, 977, 1069, 1097, 1103, 1123, 1187, 1223, 1283, 1367, 1433, 1453, 1459, 1493, 1499, 1511, 1613, 1709, 1747, 1753, 1759, 1789, 1889, 1907, 2099, 2161
Offset: 1

Views

Author

Rémi Eismann, Feb 03 2007

Keywords

Comments

This sequence is equal to 13, 31, A006562, A117876, A118467, ..., A125623, ... Let p(n) denote the n-th prime. If 2 p(n) - p(n+1) is a prime, say p(n-i) and if p(n) has a level 1 in A117563, then we say that p(n) has level(1,i). Primes of level (1,1) form the sequence A006562. 13 and 31 have a level 1 but not sublevel i.

Links

Crossrefs

Cf. A006562, A117876, A118467, A125623, A119402, A118464, A125576.

A119402 Primes p=prime(i) of level (1,11), i.e., such that A118534(i)=prime(i-11).

Original entry on oeis.org

576791, 3361517, 9433859, 10460719, 11630503, 11707537, 12080027, 19743677, 28716287, 33384517, 34961923, 36627659, 37776967, 38087983, 40794049, 45650359, 49152757, 52230229, 53152907, 53240927, 55036789, 56167103, 56177783, 57717749, 58804483, 71849423, 76119269
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jul 25 2006

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,11): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(240963) - prime(240962) = 3361601 - 3361517 = 3361517 - 3361433 = prime(240962) - prime(240962-11) and prime(240962) has level 1 in A117563, so prime(240962)=3361517 has level (1,11).

Links

Crossrefs

Cf. A006562 (primes of level (1,1)), A117078, A117563, A006562, A117876, A118464, A118467.

Extensions

More terms from Fabien Sibenaler, Oct 20 2006
Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A119403 Primes p=prime(i) of level (1,10), i.e., such that A118534(i)=prime(i-10).

Original entry on oeis.org

745757, 1103639, 1583369, 1895359, 2124049, 3327419, 4234537, 4437779, 5071973, 6287647, 7702573, 8470927, 8675923, 9493151, 9750079, 10868203, 11213843, 14244173, 14796253, 14978893, 15611909, 16489273, 17528681, 18280771, 19125163, 19403831, 19631411, 21975167
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jul 25 2006

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,10): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(353166) - prime(353165) = 5072057 - 5071973 = 5071973 - 5071889 = prime(353165) - prime(353165-10) and prime(353165) has level 1 in A117563, so prime(353165)=5071973 has level (1,10).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467.

Programs

  • PARI
    lista(nn) = my(c=11, v=primes(11)); forprime(p=37, nn, if(2*v[c]-p==v[c=c%11+1], print1(precprime(p-1), ", ")); v[c]=p); \\ Jinyuan Wang, Jun 18 2021

Extensions

More terms from Fabien Sibenaler, Oct 20 2006
Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A119404 Primes p=prime(i) of level (1,9), i.e., such that A118534(i)=prime(i-9).

Original entry on oeis.org

678659, 855739, 1403981, 2366543, 2744783, 2830657, 3027539, 3317033, 4525909, 4676851, 5341463, 5819563, 7087123, 7181897, 8815663, 9324257, 9878929, 9976937, 10403251, 10440641, 10447457, 10766411, 10787377, 11829151, 11881957, 12539389, 14026433, 14087179
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jul 25 2006

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,9): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(780815) - prime(780814) = 11882071 - 11881957 = 11881957 - 11881843 = prime(780814) - prime(780814-9) and prime(780814) has level 1 in A117563, so prime(780814)=11881957 has level (1,9).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467.

Extensions

Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A125576 Primes p=prime(i) of level (1,15), i.e., such that A118534(i)=prime(i-15).

Original entry on oeis.org

264426203, 295902073, 361949821, 704544167, 1075639757, 1259347393, 1290546427, 1301756207, 1335396547, 1370742383, 1460811643, 1497078991, 1514647247, 1643839649, 1783137281, 2142070103, 2424093281, 2471124197, 2494743721, 2577014057, 2706824389, 2951139253
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jan 27 2007

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,15): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(16042282) - prime(16042281) = 295902247 - 295902073 = 295902073 - 295901899 = prime(16042281) - prime(16042281-15) and prime(16042281) has level 1 in A117563, so prime(16042281)=295902073 has level (1,15).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404.

Programs

  • PARI
    lista(nn) = my(c=16, v=primes(16)); forprime(p=59, nn, if(2*v[c]-p==v[c=c%16+1], print1(precprime(p-1), ", ")); v[c]=p); \\ Jinyuan Wang, Jun 18 2021

Extensions

Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009
Terms a(5) and beyond from b-file by Andrew Howroyd, Feb 05 2018

A125623 Primes p=prime(i) of level (1,16), i.e., such that A118534(i)=prime(i-16).

Original entry on oeis.org

356604959, 613768081, 709208323, 950803363, 979872743, 1174872271, 1186433617, 1625945609, 1796767963, 1840621901, 2348698453, 2547482281, 3385901059, 3446679371, 3512406283, 3735873397, 4080198391, 4106437259, 4319987921, 4695419887, 5285414713, 5288810297
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jan 27 2007

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,16): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(48470200) - prime(48470199) = 950803519 - 950803363 = 950803363 - 950803207 = prime(48470199) - prime(48470199-16) and prime(48470199) has level 1 in A117563, so prime(48470199) = 950803363 has level (1,16).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404.

Programs

  • PARI
    lista(nn) = my(v=primes(17)); forprime(p=61, nn, if(2*v[17]-p==v[1], print1(v[17], ", ")); v=concat(v[2..17], p)); \\ Jinyuan Wang, Jun 18 2021

Extensions

Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A125565 Primes p=prime(i) of level (1,12), i.e., such that A118534(i)=prime(i-12).

Original entry on oeis.org

15014557, 27001043, 29602093, 50234633, 87028433, 91814759, 94529221, 103336843, 112840309, 113774329, 113961299, 114887657, 115528969, 118974901, 129235273, 144352123, 146127721, 160370491, 163559197, 169274999, 188168059, 188895919, 191829409, 198823447
Offset: 1

Views

Author

Rémi Eismann, Jan 27 2007

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,12): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(5316164) - prime(5316163) = 91814831 - 91814759 = 91814759 - 91814687 = prime(5316163) - prime(5316163-12) and prime(5316163) has level 1 in A117563, so prime(5316163)=91814759 has level (1,12).

Links

Crossrefs

Cf. A006562 (primes of level (1,1)), A117078, A117563, A006562, A117876, A118464, A118467, A119402, A119403, A119404.

Extensions

Definition and comment reworded following suggestions from the author. - M. F. Hasler, Nov 30 2009

A125572 Primes p=prime(i) of level (1,13), i.e., such that A118534(i)=prime(i-13).

Original entry on oeis.org

35630467, 118877047, 123823081, 140061577, 155032793, 175204303, 184606997, 188871349, 189489733, 232093339, 244004749, 278518081, 309055367, 310542257, 313596551, 315659909, 329918227, 340761691, 389220347, 398329523, 411405833, 422745641, 480428801, 485608819
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jan 27 2007

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,13): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(10272256) - prime(10272255) = 184607153 - 184606997 = 184606997 - 184606841 = prime(10272255) - prime(10272255-13) and prime(10272255) has level 1 in A117563, so prime(10272255)=184606997 has level (1,13).

Links

Crossrefs

Cf. A006562 (primes of level (1,1)), A117078, A117563, A117876, A118464, A118467, A119402, A119403, A119404.

Extensions

Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A125574 Primes p=prime(i) of level (1,14), i.e., such that A118534(i)=prime(i-14).

Original entry on oeis.org

31515413, 69730637, 132102911, 132375259, 215483129, 284491367, 325689253, 388190689, 548369603, 620829113, 633418787, 638213603, 670216277, 793852487, 797759539, 960200149, 1038197399, 1050359137, 1092920249, 1331713301, 1342954871, 1349496367, 1365964199
Offset: 1

Views

Author

Rémi Eismann and Fabien Sibenaler, Jan 27 2007

Keywords

Comments

This subsequence of A125830 and of A162174 gives primes of level (1,14): If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

Examples

			prime(15456800) - prime(15456799) = 284491601 - 284491367 = 284491367 - 284491133 = prime(15456799) - prime(15456799-14) and prime(15456799) has level 1 in A117563, so prime(15456799) = 284491367 has level (1,14).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404.

Programs

  • PARI
    lista(nn) = my(c=15, v=primes(15)); forprime(p=53, nn, if(2*v[c]-p==v[c=c%15+1], print1(precprime(p-1), ", ")); v[c]=p); \\ Jinyuan Wang, Jun 18 2021

Extensions

Definition and comment reworded following suggestions from the authors. - M. F. Hasler, Nov 30 2009

A089344 Smallest prime(k) such that prime(k)-prime(k-n) is equal to prime(k+1)-prime(k).

Original entry on oeis.org

5, 7, 619, 6581, 13933, 15823, 22307, 259033, 678659, 745757, 576791, 15014557, 35630467, 31515413, 264426203, 356604959, 364058659, 2529682091, 6868844179, 1457908691, 12799238129, 23294528897, 72106293983, 82160403553, 230966323927, 19187736221
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2003

Keywords

Examples

			a(4) = 6581, the next prime is 6599, 6599-6581 = 18, the four previous primes are 6563, 6569, 6571 and 6577. 6581-6563 = 18.

Links

Crossrefs

Cf. A066496, A006562 (balanced primes), A117876, A118467.

Programs

  • Mathematica
    f[n_] := Block[{k = n + 1}, While[ 2Prime[k] != Prime[k + 1] + Prime[k - n], k++ ]; Prime[k]]; Table[ f[n], {n, 17}] (* Robert G. Wilson v, Nov 11 2003 *)

Formula

a(n) = prime(A066496(n)). - Giovanni Resta, Apr 04 2017

Extensions

Corrected and extended by Ray Chandler and Robert G. Wilson v, Nov 07 2003
a(18)-a(21) from Fabien Sibenaler, Mar 15 2013
a(22)-a(26) from Giovanni Resta, Apr 04 2017
Showing 1-10 of 15 results. Next

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