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 1-2 of 2 results.

A363167 Products of four distinct strong primes.

Original entry on oeis.org

200651, 222343, 283679, 319957, 363341, 385033, 408221, 428417, 452353, 463573, 483923, 491249, 513689, 526031, 544357, 546601, 547723, 580261, 605693, 671143, 688721, 696377, 698819, 739211, 740333, 742951, 743699, 747881, 771661, 774367, 783343, 790801, 808027, 820369
Offset: 1

Views

Author

Massimo Kofler, Sep 07 2023

Keywords

Comments

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

Examples

			200651 = 11*17*29*37 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 37 > (31+41)/2.
222343 = 11*17*29*41 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2, 41 > (37+43)/2.
283679 = 11*17*37*41 and 11 > (7+13)/2, 17 > (13+19)/2, 37 > (31+41)/2, 41 > (37+43)/2.

Crossrefs

Cf. A046386, A051634, A364778, A363782.

Programs

  • Mathematica
    strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 10^6, 2], (f = FactorInteger[#])[[;; , 2]] == {1, 1, 1, 1} && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Sep 08 2023 *)

A364778 Products of two distinct strong primes.

Original entry on oeis.org

121, 187, 289, 319, 407, 451, 493, 629, 649, 697, 737, 781, 841, 869, 1003, 1067, 1073, 1111, 1139, 1177, 1189, 1207, 1343, 1369, 1397, 1507, 1517, 1639, 1649, 1681, 1711, 1717, 1793, 1819, 1943, 1969, 2059, 2101, 2159, 2167, 2183, 2291, 2329, 2419, 2453, 2479, 2497, 2533, 2627, 2629, 2747
Offset: 1

Views

Author

Massimo Kofler, Aug 07 2023

Keywords

Comments

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

Examples

			121 = 11^2 and 11 > (7+13)/2.
187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2.
493 = 17*29 and 17 > (13+19)/2, 29 > (23+31)/2.

Crossrefs

Cf. A001358, A051634, A363167, A363782.

Programs

  • Mathematica
    strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], MemberQ[{{1, 1}, {2}}, (f = FactorInteger[#])[[;; , 2]]] && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Aug 07 2023 *)

Extensions

Definition clarified by N. J. A. Sloane, Oct 08 2023
Showing 1-2 of 2 results.

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

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