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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A133347 a(n) = smallest k such that prime(n+3) = prime(n) + (prime(n) mod k), or 0 if no such k exists.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 19, 27, 29, 27, 33, 39, 47, 49, 55, 59, 19, 61, 65, 15, 29, 31, 31, 29, 29, 89, 23, 113, 41, 121, 15, 27, 47, 21, 17, 31, 15, 33, 61, 25, 57, 57, 193, 71, 43, 31, 43, 221, 73, 233, 27, 83, 257, 37, 29, 51, 51, 21, 11, 97, 289, 41, 313, 107, 67
Offset: 1

Views

Author

Rémi Eismann, Oct 20 2007

Keywords

Examples

			For n = 1 we have prime(n) = 2, prime(n+3) = 7; there is no k such that 7 - 2 = 5 = (2 mod k), hence a(1) = 0.
For n = 10 we have prime(n) = 29, prime(n+3) = 41; 17 is the smallest k such that 41 - 29 = 12 = (29 mod k), hence a(10) = 17.
For n = 53 we have prime(n) = 241, prime(n+3) = 263; 73 is the smallest k such that 263 - 241 = 22 = (241 mod k), hence a(53) = 73.

Links

Crossrefs

Cf. A000040, A117078, A117563, A001223, A118534, A020639, A090369, A090368, A130533, A130650, A130703, A130889, A130882.

A184726 a(n) = A005408(n-1)/A090368(n-1) for n > 2 and a(n) = 0 for n <= 2.

Original entry on oeis.org

0, 0, 1, 1, 1, 3, 1, 1, 5, 1, 1, 7, 1, 5, 9, 1, 1, 11, 7, 1, 13, 1, 1, 15, 1, 7, 17, 1, 11, 19, 1, 1, 21, 13, 1, 23, 1, 1, 25, 11, 1, 27, 1, 17, 29, 1, 13, 31, 19, 1, 33, 1, 1, 35, 1, 1, 37, 1, 23, 39, 17, 11, 41, 25, 1, 43, 1, 19, 45, 1, 1, 47
Offset: 1

Views

Author

Rémi Eismann, Jan 20 2011

Keywords

Comments

a(n) is the "level" of odd numbers.
The decomposition of odd numbers into weight * level + gap is A005408(n) = A090368(n-1) * a(n) + 2 if a(n) > 0.

Examples

			For n = 3 we have A005408(2)/A090368(2)= 3 / 3 = 1; hence a(3) = 1.
For n = 24 we have A005408(23)/A090368(23)= 45 / 3 = 14; hence a(24) = 15.

Links

Crossrefs

Cf. A005408, A090368, A117078, A117563, A001223.

A184727 a(n) = A005843(n-1)/A090369(n-1) for n > 2 and a(n) = 0 for n <= 2.

Original entry on oeis.org

0, 0, 1, 2, 2, 2, 4, 2, 4, 6, 5, 2, 8, 2, 7, 10, 8, 2, 12, 2, 10, 14, 11, 2, 16, 10, 13, 18, 14, 2, 20, 2, 16, 22, 17, 14, 24, 2, 19, 26, 20, 2, 28, 2, 22, 30, 23, 2, 32, 14, 25, 34, 26, 2, 36, 22, 28, 38, 29, 2, 40, 2, 31, 42, 32, 26
Offset: 1

Views

Author

Rémi Eismann, Jan 20 2011

Keywords

Comments

a(n) is the "level" of even numbers.
The decomposition of even numbers into weight * level + gap is A005843(n) = A090369(n-1) * a(n) + 2 if a(n) > 0.

Examples

			For n = 3 we have A005843(2)/A090369(2)= 4 / 4 = 1; hence a(3) = 1.
For n = 24 we have A005843(23)/A090369(23)= 46 / 23 = 2; hence a(24) = 2.

Links

Crossrefs

Cf. A005843, A090369, A117078, A117563, A001223.

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 71-77 of 77 results.

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