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 12 results. Next

A118924 Primes for which the weight as defined in A117078 is 53 and the gap as defined in A001223 is 52.

Original entry on oeis.org

19609, 547171, 3099757, 3282289, 3401221, 4286851, 4648099, 5544859, 5622769, 5731207, 5868901, 6387559, 6581857, 6949147, 6985081, 7382899, 7412791, 7675141, 7697401, 8203021, 8366791, 9190411, 9649921, 9990499, 9994951
Offset: 1

Views

Author

Rémi Eismann, May 25 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (106i-1) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			Prime(2226) = prime(2225) + (prime(2225) mod 53) = 19609 + (19609 mod 53) = 19661
g(n) = 19661 - 19609 = 53 - 1 = 52

Crossrefs

Cf. A117078, A001223, A001359, A117563, A074822, A118922, A118359, A118924, A119504, A119597, A119596, A119595, A118380.

A118359 Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 6.

Original entry on oeis.org

83, 167, 251, 433, 503, 587, 601, 727, 1063, 1217, 1231, 1553, 1777, 1861, 1973, 1987, 2281, 2351, 2393, 2897, 3541, 4073, 4283, 4451, 4507, 4591, 4871, 5081, 5431, 5557, 5641, 5683
Offset: 1

Views

Author

Rémi Eismann, May 24 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (14i-1) with i=(level(n)+1)/2, level(n) defined in A117563. level(n) is not multiple of 3.

Examples

			prime(24) = prime (23) + prime(23)mod(7) = prime (23) + prime(23)mod(77)
89 = 83 + 83mod(7) = 83 + 83mod(77)
k=7, level = 77/7 = 11

Links

Crossrefs

Cf. A117078, A117563, A001359, A074822, A118922, A118924, A119504, A119597, A119596, A119595.

A119504 Primes for which the weight as defined in A117078 is 23.

Original entry on oeis.org

631, 773, 2467, 2833, 3121, 3203, 3347, 3617, 4219, 4733, 4909, 4951, 5273, 6619, 7027, 7129, 7529, 8263, 8783, 9049, 9413, 9643, 9649, 10891, 11483, 11719, 12541, 13093, 13183, 13841, 14243, 14293, 14851, 15121, 15629, 15667, 15671, 15761
Offset: 1

Views

Author

Rémi Eismann, May 27 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (56i-23+gap) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			a(1) = prime(115) = 631 because prime(116) = prime(115) + (prime(115) mod 53) = 641
g(n) = 641 - 631 = 10
Prime(115) + 23 - 10 = 644, 644/46 = 14

Links

Crossrefs

Cf. A117078, A118359, A001359, A118380, A118924, A118922.

Formula

A117078 : a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists. prime(n) for which k=23.

A119595 Primes for which the weight as defined in A117078 is 15 and the gap as defined in A001223 is 8.

Original entry on oeis.org

743, 1193, 1523, 1733, 2003, 2243, 2273, 3623, 4583, 4943, 5573, 5693, 6143, 6203, 6473, 7673, 8573, 8933, 9803, 10103, 11243, 11813, 12413, 12503, 13163, 14423, 14843, 15053, 15233, 15383, 16103
Offset: 1

Views

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (30i-7) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			a(1)=743 because of 751=743+mod(743;15) and g(n)=751-743=8
30*((49+1)/2)-7=743
a(2)=1193 because of 1201=1193+mod(1193;15) and g(n)=1201-1193=8
30*((79+1)/2)-7=1193

Links

Crossrefs

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

A119596 Primes for which the weight as defined in A117078 is 11 and the gap as defined in A001223 is 10.

Original entry on oeis.org

241, 1627, 2089, 4201, 4663, 4861, 5323, 6247, 6379, 6709, 8821, 9283, 9679, 10141, 12253, 12517, 12781, 13441, 15091, 15289, 15619, 17599, 17929, 19249, 19447, 19843, 21757, 23539, 26839, 28687, 33703, 34429, 34693, 35089, 35353, 36343
Offset: 1

Views

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (22i-1) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			a(1)=241 because of 251=241+mod(241;11) and 251-241=10.
22*((21+1)/2)-1=241, level=21
a(2)=1627 because of 1637=1627+mod(1627;11) and 1637-1627=10
22*((147+1)/2)-1=1627, level=147

Links

Crossrefs

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

A119597 Primes for which the weight as defined in A117078 is 11 and the gap as defined in A001223 is 6.

Original entry on oeis.org

61, 677, 941, 1117, 1601, 2063, 2371, 3691, 3911, 4021, 5297, 5407, 6067, 6353, 6991, 7541, 7717, 8311, 8641, 8663, 9103, 9851, 10973, 11897, 12491, 12953, 13591, 13613, 13723, 14537, 15131, 15263, 15307, 15461, 15901, 16363
Offset: 1

Views

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (22i-5) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			a(1)=61 because of 67=61+mod(61;11) and 67-61=6.
22*((5+1)/2)-5=61, level=5
a(2)=677 because of 683=677+mod(677;11) and 683-677=6
22*((61+1)/2)-5=677, level=5

Links

Crossrefs

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

A118741 Primes for which the weight as defined in A117078 is 7.

Original entry on oeis.org

67, 83, 167, 193, 251, 277, 433, 487, 503, 587, 601, 613, 727, 823, 907, 1063, 1217, 1231, 1553, 1663, 1777, 1861, 1873, 1973, 1987, 2083, 2281, 2293, 2351, 2377, 2393, 2797, 2897, 3217, 3343, 3541, 3847, 4073, 4283, 4451, 4507, 4591, 4813, 4871, 5081
Offset: 1

Views

Author

Rémi Eismann, May 22 2006; May 27 2006; May 04 2007

Keywords

Comments

The gap as defined in A001223 of this prime numbers is 4 or 6.
The prime numbers in this sequence are of the form (14i-1) (if gap=6) or (14i-3) (if gap=4) with i=(level(n)+1)/2, level(n) defined in A117563.

Links

Crossrefs

Cf. A117078, A117563, A118922, A118924.

Programs

  • Mathematica
    f[n_] := Block[{a, p = Prime[n], np = Prime[n + 1]}, a = Min[Select[Divisors[2*p - np], #1 > np - p & ]]; If[a == Infinity, 0, a]]; Prime@ Select[ Range@695, f@# == 7 &] (* Robert G. Wilson v, May 26 2006 *)

Formula

A117078 : a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists. prime(n) for which k=7.

Extensions

More terms from Robert G. Wilson v, May 26 2006

A119593 Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.

Original entry on oeis.org

67, 193, 277, 487, 613, 823, 907, 1663, 1873, 2083, 2293, 2377, 2797, 3217, 3343, 3847, 4813, 5233, 5527, 5653, 5737, 6577, 6997, 7207, 7753, 8677, 8803, 9433, 11113, 11617
Offset: 1

Views

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (14i-3) with i=(level(n)+1)/2, level(n) defined in A117563.

Links

Crossrefs

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

Programs

  • PARI
    forprimestep(p=67,1e4,14, t=p%5; if((t==2 || t==3) && isprime(p+4), print1(p", "))) \\ Charles R Greathouse IV, Sep 17 2022
  • PARI
    p=67; forprime(q=p+2,1e4, if(q-p==4 && (p%70==53 || p%70==67), print1(p", ")); p=q) \\ Charles R Greathouse IV, Sep 17 2022

Formula

Primes p such that (1) p = 53 or 67 mod 70 and (2) p+4 is prime. - Charles R Greathouse IV, Sep 17 2022
a(n) = Omega(n log^2 n). - Charles R Greathouse IV, Sep 17 2022

A119594 Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 4.

Original entry on oeis.org

13, 103, 463, 643, 877, 967, 1093, 1597, 1867, 1993, 2137, 2857, 3037, 3163, 3253, 3613, 3793, 4153, 4513, 4783, 5413, 5503, 5647, 6007, 6043, 6547, 6907, 7537, 7573, 7933, 8167, 8293, 9157, 9337, 9463, 9787
Offset: 1

Views

Author

Rémi Eismann, Jun 01 2006, May 04 2007

Keywords

Comments

The prime numbers in this sequence are of the form (18i-5) with i=(level(n)+1)/2, level(n) defined in A117563.

Examples

			a(1)=13 because of 17=13+mod(13;9) and 17-13=4.
18*1-5=13, level=1
a(2)=103 because of 107=103+mod(103;9) and 107-103=4
18*((11+1)/2)-5=103, level=11

Links

Crossrefs

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

A132253 Isolated primes congruent to 29 (mod 30).

Original entry on oeis.org

89, 359, 389, 449, 479, 509, 719, 839, 929, 1109, 1259, 1409, 1439, 1499, 1559, 1709, 1889, 1979, 2039, 2069, 2099, 2399, 2459, 2579, 2609, 2699, 2819, 2879, 2909, 2939, 3089, 3209, 3449, 3659, 3719, 3779, 3989, 4079, 4139, 4289, 4349
Offset: 1

Views

Author

Omar E. Pol, Aug 20 2007

Keywords

Links

Crossrefs

Cf. A007510, A031926, A118922.

Programs

  • Mathematica
    Select[Range[29,4500,30],PrimeQ[#]&&NoneTrue[#+{2,-2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 13 2018 *)
Showing 1-10 of 12 results. Next

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