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.

A060421 Numbers k such that the first k digits of the decimal expansion of Pi form a prime.

Original entry on oeis.org

1, 2, 6, 38, 16208, 47577, 78073, 613373
Offset: 1

Views

Author

Michel ten Voorde, Apr 05 2001

Keywords

Comments

The Brown link states that in 2001 Ed T. Prothro reported discovering that 16208 gives a probable prime and that Prothro verified that all values for 500 through 16207 digits of Pi are composites. - Rick L. Shepherd, Sep 10 2002
The corresponding primes are in A005042. - Alexander R. Povolotsky, Dec 17 2007

Examples

			3 is prime, so a(1) = 1; 31 is prime, so a(2) = 2; 314159 is prime, so a(3) = 6; ...

Links

Crossrefs

Cf. A000796 (Pi), A005042, A007523, A047658.
Primes in other constants: A064118 (e), A065815 (gamma), A064119 (phi), A118328 (Catalan's constant), A115377 (sqrt(2)), A119344 (sqrt(3)), A228226 (log 2), A228240 (log 10), A119334 (zeta(3)), A122422 (Soldner's constant), A118420 (Glaisher-Kinkelin constant), A174974 (Golomb-Dickman constant), A118327 (Khinchin's constant).
In other bases: A065987 (binary), A065989 (ternary), A065991 (quaternary), A065990 (quinary), A065993 (senary).

Programs

  • Mathematica
    Do[If[PrimeQ[FromDigits[RealDigits[N[Pi, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 9016} ]

Extensions

a(6) = 47577 from Eric W. Weisstein, Apr 01 2006
a(7) = 78073 from Eric W. Weisstein, Jul 13 2006
a(8) = 613373 from Adrian Bondrescu, May 29 2016

A064117 Primes formed by the initial digits of the decimal expansion of the golden ratio phi = (1+sqrt(5))/2.

Original entry on oeis.org

1618033, 1618033988749
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 09 2001

Keywords

Comments

The next terms are too large to include here, see A064119.

Links

Crossrefs

Cf. A064119.

Extensions

Incorrect comment removed by Felix Fröhlich, Aug 25 2014
Definition adjusted by Felix Fröhlich, Aug 25 2014

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 1-3 of 3 results.

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

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