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.

Previous Showing 11-18 of 18 results.

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

A098029 Primes of the form (prime(k)+ prime(k+3))/2.

Original entry on oeis.org

7, 23, 37, 47, 67, 73, 233, 277, 353, 479, 613, 631, 647, 809, 1097, 1283, 1297, 1433, 1453, 1471, 1493, 1607, 1613, 1663, 1709, 1721, 1783, 1867, 1889, 1901, 1931, 1993, 2099, 2137, 2161, 2377, 2383, 2411, 2521, 2621, 2683, 2693, 2713, 2797, 2879, 3049
Offset: 1

Views

Author

Cino Hilliard, Sep 10 2004

Keywords

Comments

The union of {7}, A119381 and A117876. - Irina Gerasimova, Jul 11 2013

Examples

			prime(2)=3, prime(2+3)=11. (3+11)/2 = 7

Links

Programs

  • Mathematica
    Select[(#[[1]]+#[[4]])/2&/@Partition[Prime[Range[500]],4,1],PrimeQ] (* Harvey P. Dale, Nov 30 2017 *)
  • PARI
    f(n,m) = for(x=1,n,y=prime(x)+prime(x+m);if(y%2==0 & isprime(y\2), print1(y\2",")))

A118481 Primes for which the level is equal to 9 in A117563.

Original entry on oeis.org

29, 67, 89, 181, 293, 811, 919, 1153, 1801, 2017, 2053, 2113, 2647, 3373, 3469, 3583, 4057, 5153, 5581, 6481, 6553, 7727, 8209, 8447, 8467, 8543, 8867, 9887, 10009, 10477, 11027, 11743, 12601, 13249, 13421, 13729, 13789, 15017, 15391, 17011, 17123, 18919
Offset: 1

Views

Author

Rémi Eismann, May 05 2006

Keywords

Examples

			Prime(310) has level 9: prime(311) = prime(310)+prime(310) mod(227) = prime(310)+prime(310) mod(2043) = 2063

Links

Crossrefs

Cf. A117563, A117873, A117078, A117874, A006562, A117876, A001359, A118464.

Extensions

Edited by N. J. A. Sloane, May 14 2006
Term a(19) and beyond from b-file by Andrew Howroyd, Feb 05 2018

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
Previous Showing 11-18 of 18 results.

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

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