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 1-3 of 3 results.

A234105 Integers of the form (p*q*r*s - 1)/2, where p, q, r, s are distinct primes.

Original entry on oeis.org

577, 682, 892, 997, 1072, 1207, 1402, 1501, 1522, 1567, 1627, 1657, 1852, 1897, 1942, 1963, 2152, 2194, 2242, 2257, 2320, 2392, 2422, 2467, 2502, 2557, 2593, 2656, 2782, 2827, 2932, 3022, 3052, 3097, 3139, 3202, 3272, 3277, 3349, 3382, 3391, 3517, 3547, 3580
Offset: 1

Views

Author

Clark Kimberling, Jan 01 2014

Keywords

Crossrefs

Cf. A234498, A234499, A234500, A234093, A234097.

Programs

  • Mathematica
    t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t - 1)/2, 120] (* A234105 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234498 *)
(w - 1)/2 (* A234499 *) (* Peter J. C. Moses, Dec 23 2013 *)

Formula

-1 + A234500.

A234499 Primes of the form (p*q*r*s - 1)/2, where p, q, r,s are distinct primes.

Original entry on oeis.org

577, 997, 1567, 1627, 1657, 2467, 2557, 2593, 3391, 3517, 3547, 3607, 3697, 3727, 3877, 4231, 4273, 4357, 4933, 5167, 5227, 5347, 5407, 5527, 5857, 5869, 6121, 6451, 7297, 7417, 7927, 8053, 8179, 8389, 8431, 8521, 8627, 8677, 9091, 9397, 9439, 9547, 9613
Offset: 1

Views

Author

Clark Kimberling, Jan 01 2014

Keywords

Examples

			(See A234498.)

Links

Crossrefs

Cf. A234105, A234499, A234500.

Programs

  • Mathematica
    t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t - 1)/2, 120] (* A234105 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234498 *)
(w - 1)/2 (* A234499 *) (* Peter J. C. Moses, Dec 23 2013 *)
Module[{upto=10000,maxp},maxp=Ceiling[PrimePi[upto/30]];Select[Sort[ Select[ (#-1)/2&/@Times@@@Subsets[Prime[Range[maxp]],{4}], PrimeQ]], #<=upto&]] (* Harvey P. Dale, Feb 07 2016 *)

A234501 Products p*q*r*s of distinct primes for which (p*q*r*s + 1)/2 is prime.

Original entry on oeis.org

1365, 3045, 4305, 4485, 4785, 4845, 5005, 5313, 6045, 6405, 7161, 7665, 8265, 8745, 9165, 9345, 9933, 10005, 10101, 10465, 10545, 10605, 10965, 11305, 11685, 12441, 12597, 13585, 14385, 14421, 14973, 15045, 15405, 15645, 15873, 16185, 16485, 17085, 17385
Offset: 1

Views

Author

Clark Kimberling, Jan 01 2014

Keywords

Examples

			1365 = 3*5*7*13, and (1365+1)/2 = 683, a prime.

Crossrefs

Cf. A234500, A234502, A234498, A234103.

Programs

  • Mathematica
    t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*)
v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234501 *)
(w + 1)/2 (* A234502 *)   (* Peter J. C. Moses, Dec 23 2013 *)
Showing 1-3 of 3 results.

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

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