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.

A165571 Lesser prime factor of successively better golden semiprimes.

Original entry on oeis.org

2, 3, 7, 19, 23, 29, 97, 353, 563, 631, 919, 1453, 2207, 15271, 15737, 42797, 49939, 133559, 179317, 287557, 508451, 918011, 1103483, 1981891, 9181097, 16958611, 17351447, 52204391, 66602803, 99641617, 134887397, 487195147, 629449511, 943818943, 1527963169, 2048029369
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2009

Keywords

Comments

See A165569 and A165570 for the definition. Probably a subset of A108541.

Links

Crossrefs

Cf. A108539, A165569, A165570, A165572.

Programs

  • Mathematica
    f[p_] := Module[{x = GoldenRatio * p, p1, p2}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; If[p2 - x > x - p1, p1, p2]]; seq={}; dm = 1; p1 = 1; Do[p1 = NextPrime[p1]; k++; p2 = f[p1]; d = Abs[p2/p1 - GoldenRatio]; If[d < dm, dm = d; AppendTo[seq, p1]], {10^4}]; seq  (* Amiram Eldar, Nov 28 2019 *)

Formula

a(n) = A000040(A165569(n)).
a(n) = A165570(n)/A165572(n).

Extensions

a(16)-a(23) from Donovan Johnson, May 13 2010
a(24)-a(36) from Amiram Eldar, Nov 28 2019

A165572 Greater prime factor of successively better golden semiprimes.

Original entry on oeis.org

3, 5, 11, 31, 37, 47, 157, 571, 911, 1021, 1487, 2351, 3571, 24709, 25463, 69247, 80803, 216103, 290141, 465277, 822691, 1485373, 1785473, 3206767, 14855327, 27439609, 28075231, 84468479, 107765599, 161223523, 218252393, 788298307, 1018470703, 1527131129, 2472296341
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2009

Keywords

Comments

See A165569 and A165570 for the definition. Probably a subset of A108542.

Links

Crossrefs

Cf. A108539, A165569, A165570, A165571.

Programs

  • Mathematica
    f[p_] := Module[{x = GoldenRatio * p, p1, p2}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; If[p2 - x > x - p1, p1, p2]]; seq={}; dm = 1; p1 = 1; Do[p1 = NextPrime[p1]; k++; p2 = f[p1]; d = Abs[p2/p1 - GoldenRatio]; If[d < dm, dm = d; AppendTo[seq, p2]], {10^4}]; seq  (* Amiram Eldar, Nov 28 2019 *)

Formula

a(n) = A108539(A165569(n)).
a(n) = A165570(n)/A165571(n).

Extensions

a(16)-a(23) from Donovan Johnson, May 13 2010
a(24)-a(35) from Amiram Eldar, Nov 28 2019

A165569 The indexing sequence for successively better golden semiprimes.

Original entry on oeis.org

1, 2, 4, 8, 9, 10, 25, 71, 103, 115, 157, 231, 329, 1783, 1835, 4476, 5128, 12462, 16274, 25035, 42174, 72589, 85968, 147666, 613726, 1088825, 1112415, 3125316, 3929736, 5742036, 7639447, 25716100, 32780150, 48132247, 76049401, 100464259, 108803364, 186018939
Offset: 1

Views

Author

Antti Karttunen, Sep 22 2009

Keywords

Links

Crossrefs

The corresponding semiprimes are given by A165570(n) = A165571(n)*A165572(n).
Cf. A108539.

Programs

  • Mathematica
    f[p_] := Module[{x = GoldenRatio * p, p1, p2}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; If[p2 - x > x - p1, p1, p2]]; seq={}; k=0; dm = 1; p1 = 1; Do[p1 = NextPrime[p1]; k++; p2 = f[p1]; d = Abs[p2/p1 - GoldenRatio]; If[d < dm, dm = d; AppendTo[seq, k]], {10^4}]; seq (* Amiram Eldar, Nov 28 2019 *)

Formula

a(1)=1, and for n>1, a(n) = first such i>a(n-1) that abs(phi - A108539(i)/A000040(i)) < abs(phi - A108539(a(n-1))/A000040(a(n-1))), where phi = (1+sqrt(5))/2 (Golden ratio).

Extensions

a(16)-a(38) from Amiram Eldar, Nov 28 2019
Showing 1-3 of 3 results.

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