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.

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A064119 Numbers k such that the first k digits of the Golden Ratio form a prime.

Original entry on oeis.org

7, 13, 255, 280, 97241
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 09 2001

Keywords

Examples

			a(1)=7 because the 7-digit number 1618033 is prime.

Links

Crossrefs

Cf. A064117.

Programs

  • Mathematica
    Do[If[PrimeQ[ FromDigits[RealDigits[N[GoldenRatio, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 3000}]
With[{gr=RealDigits[GoldenRatio,10,100000][[1]]},Select[Range[ 100000], PrimeQ[ FromDigits[Take[gr,#]]]&]] (* Harvey P. Dale, Jul 24 2016 *)

Extensions

a(5) = 97241 from Eric W. Weisstein, Jun 04 2009

A276198 Smallest prime >= decimal expansion of phi truncated to n places (A011551), where phi is the golden ratio (A001622).

Original entry on oeis.org

2, 17, 163, 1619, 16183, 161807, 1618033, 16180349, 161803403, 1618033999, 16180339933, 161803398917, 1618033988749, 16180339887557, 161803398874991, 1618033988749901, 16180339887498961, 161803398874989661, 1618033988749894853, 16180339887498948503, 161803398874989484891
Offset: 0

Views

Author

Ilya Gutkovskiy, Aug 24 2016

Keywords

Examples

			a(5) = 161807, since this is the smallest prime >= floor(phi*10^5) = 161803.
phi = 1.61803398874989484820458683436563811772...

Links

Crossrefs

Cf. A000040, A000720, A001622, A007918, A011551, A064117, A064119.

Programs

  • Mathematica
    Table[NextPrime[Floor[GoldenRatio 10^n] - 1], {n, 0, 20}]

Formula

a(n) = A007918(A011551(n)).
a(n) = A000040(A000720(A011551(n)-1)+1).
a(A064119(n)-1) = A064117(n).
Showing 1-2 of 2 results.

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

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