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.

User: Fabien Sibenaler

Fabien Sibenaler's wiki page.

Fabien Sibenaler has authored 13 sequences. Here are the ten most recent ones:

A216204 Primes p=prime(i) of level (1,8), i.e., such that A118534(i) = prime(i-8).

Original entry on oeis.org

259033, 308153, 343831, 377393, 576227, 597697, 780733, 990397, 1408889, 1643893, 1648613, 1678777, 1910179, 1942207, 2045377, 2049191, 2073403, 2388703, 2403701, 2430611, 2448883, 2481517, 2572529, 2710457, 2827687, 2982697, 3376859, 3404579, 3942413, 4119419
Offset: 1

Views

Author

Fabien Sibenaler, Mar 12 2013

Keywords

Comments

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).
Subsequence of A125830 and of A162174.

Examples

			343831 = prime(24490) is a term because:
prime(24491) = 343891, prime(24382) = 343771;
2*prime(24490) - prime(24491) = prime(24382).

Links

Crossrefs

Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404, A125565, A125572, A125574, A125576, A125623.

Programs

  • Mathematica
    With[{m = 8}, Prime@ Select[Range[m + 1, 2*10^5], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* Michael De Vlieger, Jul 16 2017 *)
  • PARI
    lista(nn) = my(v=primes(9)); forprime(p=29, nn, if(2*v[9]-p==v[1], print1(v[9], ", ")); v=concat(v[2..9], p)); \\ Jinyuan Wang, Jun 18 2021

A216202 Primes p=prime(i) of level (1,7), i.e., such that A118534(i) = prime(i-7).

Original entry on oeis.org

22307, 39251, 81569, 85853, 132763, 159233, 179849, 188029, 281431, 370949, 373393, 421741, 480587, 607363, 630737, 741721, 770669, 782011, 812527, 879743, 909917, 928703, 1008263, 1037347, 1095859, 1111091, 1126897, 1173631, 1260911, 1382681, 1398781, 1439447
Offset: 1

Views

Author

Fabien Sibenaler, Mar 12 2013

Keywords

Comments

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

			81569 = prime(7980) is a term because:
prime(7981) = 81611, prime(7973) = 81527;
2*prime(7980) - prime(7981) = prime(7973).

Links

Crossrefs

Subsequence of A125830 and A162174.
Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404, A125565, A125572, A125574, A125576, A125623.

Programs

  • Mathematica
    With[{m = 7}, Prime@ Select[Range[m + 1, 10^5], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* Michael De Vlieger, Jul 16 2017 *)

A216180 Primes p=prime(i) of level (1,6), i.e., such that A118534(i) = prime(i-6).

Original entry on oeis.org

15823, 21617, 31277, 43331, 65731, 97883, 100853, 120947, 265277, 318023, 320953, 361241, 362759, 419831, 422141, 426799, 452549, 465211, 482441, 491539, 504403, 513533, 526781, 540391, 551597, 557093, 575261, 582251, 598729, 649093, 654629, 663601, 678779, 782723
Offset: 1

Views

Author

Fabien Sibenaler, Mar 10 2013

Keywords

Comments

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

			31277 = prime(3373) is a term because 2*prime(3373) - prime(3374) = 2*31277 - 31307 = 31247 = prime(3367).

Links

Crossrefs

Subsequence of A125830 and of A162174.
Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404, A125565, A125572, A125574, A125576, A125623.

Programs

  • Mathematica
    With[{m = 6}, Prime@ Select[Range[m + 1, 5*10^4], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* Michael De Vlieger, Jul 16 2017 *)
  • PARI
    lista(nn) = my(c=7, v=primes(7)); forprime(p=19, nn, if(2*v[c]-p==v[c=c%7+1], print1(precprime(p-1), ", ")); v[c]=p); \\ Jinyuan Wang, Jun 18 2021

A216177 Primes p=prime(i) of level (1,4), i.e., such that A118534(i) = prime(i-4).

Original entry on oeis.org

6581, 7963, 13063, 14107, 17053, 17627, 20563, 21347, 22193, 22877, 28319, 30727, 34981, 35171, 41549, 42101, 45197, 46103, 48823, 53201, 53899, 56269, 65449, 65993, 66191, 69031, 69403, 73613, 74101, 74323, 75797, 81973, 86209, 91463, 96293, 101537, 102563
Offset: 1

Views

Author

Fabien Sibenaler, Mar 10 2013

Keywords

Comments

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

			a(2) = 7963 = prime(1006) because 2*prime(1006) - prime(1007) = 2*7963 - 7993 = 7933 = prime(1002).

Links

Crossrefs

Subsequence of A125830 and A162174.
Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404, A125565, A125572, A125574, A125576, A125623.

Programs

  • Mathematica
    With[{m = 4}, Prime@ Select[Range[m + 1, 10^4], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* Michael De Vlieger, Jul 16 2017 *)

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

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

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

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

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

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

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