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 1-5 of 5 results.

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.

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 *)

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

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 *)

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
Showing 1-5 of 5 results.

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