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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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

A118329 Catalan-primes: primes formed from the concatenation of initial decimal digits of Catalan's constant.

Original entry on oeis.org

9159655941772190150546035149323841107741493742816721
Offset: 1

Views

Author

Eric W. Weisstein, Apr 25 2006

Keywords

Comments

Next term has 276 digits and so is too large to include.

Examples

			C = 0.915965594177... and the 52-digit number a(1) = 9159655941772190150546035149323841107741493742816721 is prime.

Links

Crossrefs

Cf. A006752, A118328.

Programs

  • Mathematica
    Select[Floor[Catalan*10^Range[0, 300]], PrimeQ] (* Amiram Eldar, Jul 09 2025 *)

Formula

a(n) = floor(A006752 * 10^(A118328(n)-1)). - Amiram Eldar, Jul 09 2025

Extensions

Edited by Charles R Greathouse IV, Apr 27 2010
Showing 1-2 of 2 results.

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