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 1-4 of 4 results.

A134100 Primes p > 3 such that neither p-2 nor p-4 are prime.

Original entry on oeis.org

29, 37, 53, 59, 67, 79, 89, 97, 127, 137, 149, 157, 163, 173, 179, 191, 211, 223, 239, 251, 257, 263, 269, 277, 293, 307, 331, 337, 347, 359, 367, 373, 379, 389, 397, 409, 419, 431, 439, 449, 457, 479, 487, 499, 509, 521, 541, 547, 557, 563, 569, 577, 587
Offset: 1

Views

Author

Enoch Haga, Oct 08 2007

Keywords

Comments

Upper primes after a prime gap of 6 or larger (Union of A031925, A031927, A031929, ...) - R. J. Mathar, Mar 15 2012

Examples

			29 is a term because 29 follows the odd nonprime 27 which in turn follows the odd nonprime 25.

Links

Crossrefs

Cf. A007510, A083370, A124582, A134099, A134101, A073830.

Programs

  • Mathematica
    Select[Range[5,1000,2],PrimeQ[#]&&!PrimeQ[#-2]&&!PrimeQ[#-4]&] (* Vladimir Joseph Stephan Orlovsky, Feb 03 2012 *)
  • PARI
    forprime(p=5,600,if(!isprime(p-2) && !isprime(p-4), print1(p,", "))); \\ Joerg Arndt, Oct 27 2021
  • PARI
    list(lim)=my(v=List(),p=23); forprime(q=29,lim, if(q-p>4, listput(v,q)); p=q); Vec(v) \\ Charles R Greathouse IV, Oct 27 2021

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 27 2021

Extensions

Name corrected by Michel Marcus and Amiram Eldar, Oct 27 2021

A333200 Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.

Original entry on oeis.org

2, 3, 11, 5, 17, 29, 7, 23, 37, 97, 13, 41, 53, 367, 149, 19, 47, 59, 397, 191, 211, 31, 71, 67, 409, 251, 223, 127, 43, 83, 79, 457, 293, 479, 307, 1847, 61, 101, 89, 487, 347, 521, 331, 1949, 541, 73, 107, 137, 499, 419, 631, 787, 2129, 1087, 907, 103, 113
Offset: 1

Views

Author

Clark Kimberling, May 09 2020

Keywords

Comments

Every prime occurs exactly once.
Row 1: A001632, except for initial term
Row 2: A046132
Row 3: A031925
Row 4: A031927
Row 5: A031929
Column 1: A006512, beginning with 5,7,13

Examples

			Northwest corner:
    2   3     5    7   13   19   31   43   61   73  103
   11   17   23   41   47   71   83  101  107  113  131
   29   37   53   59   67   79   89  137  157  163  173
   97  367  397  409  457  487  499  691  709  727  751
  149  191  251  293  347  419  431  557  587  641  701

Crossrefs

Cf. A333201, A000040, A001632, A006512.

Programs

  • Mathematica
    z = 2700; p = Prime[Range[z]];
r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
TableForm[Table[Prime[r[n]], {n, 1, 18}]]  (* A333200, array *)
TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)

A126720 Primes p such that p - q = 24, where q is the previous prime before p; or prime numbers preceded by precisely 23 composite numbers.

Original entry on oeis.org

1693, 2203, 4201, 4547, 4783, 5261, 6197, 6421, 6761, 7103, 7393, 7817, 8147, 8353, 9091, 11027, 11657, 11863, 12097, 12143, 13033, 13291, 16057, 16217, 16477, 16787, 16811, 17077, 17707, 18013, 18617, 18661, 19207, 19531, 20507, 22433, 22901
Offset: 1

Views

Author

Artur Jasinski, Feb 13 2007

Keywords

Links

Crossrefs

Cf. A000230, A033560, A031505, A031925, A031927, A098974, A098976, A061779.

Programs

  • Mathematica
    a = {}; Do[If[Prime[x + 1] - Prime[x] == 24, AppendTo[a, Prime[x + 1]]], {x, 1, 10000}]; a
  • PARI
    q=2; forprime(p=3,1e5, if(p-q==24, print1(p", ")); q=p) \\ Charles R Greathouse IV, Mar 13 2020

Formula

a(n) = A098974(n) + 24. - Amiram Eldar, Mar 13 2020
a(n) >> n log^2 n. - Charles R Greathouse IV, Mar 13 2020

A243155 Larger of the two consecutive primes whose positive difference is a cube.

Original entry on oeis.org

3, 97, 367, 397, 409, 457, 487, 499, 691, 709, 727, 751, 769, 919, 937, 991, 1117, 1171, 1201, 1381, 1447, 1531, 1567, 1579, 1741, 1831, 1987, 2011, 2161, 2221, 2251, 2281, 2467, 2539, 2617, 2671, 2707, 2749, 2851, 2887, 2917, 3019, 3049, 3217, 3229, 3457, 3499
Offset: 1

Views

Author

K. D. Bajpai, May 31 2014

Keywords

Comments

Observation: All the terms in this sequence, after a(1), are the larger of the two consecutive primes which have positive difference either 2^3 or 4^3.
Superset of A031927 as the sequence contains for example numbers like 89753, 107441, 288647,.. (with gaps of 4^3...) that are not in A031927. - R. J. Mathar, Jun 06 2014

Examples

			97 is prime and appears in the sequence because 97 - 89 = 8 = 2^3.
397 is prime and appears in the sequence because 397 - 389 = 8 = 2^3.

Links

Crossrefs

Cf. A031927, A123996, A118590, A001632.

Programs

  • Maple
    A243155:= proc() local a; a:=evalf((ithprime(n+1)-ithprime(n))^(1/3)); if a=floor(a) then RETURN (ithprime(n+1)); fi; end: seq(A243155 (), n=1..100);
  • Mathematica
    n = 0; Do[t = Prime[k] - Prime[k - 1]; If[IntegerQ[t^(1/3)], n++; Print[n, " ", Prime[k]]], {k, 2, 15*10^4}]
  • PARI
    s=[]; forprime(p=3, 4000, if(ispower(p-precprime(p-1), 3), s=concat(s, p))); s \\ Colin Barker, Jun 03 2014
Showing 1-4 of 4 results.

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