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

A048796 Palindromic primes formed from decimal expansion of Pi written backwards then forwards.

Original entry on oeis.org

3, 131, 32397985356295141314159265358979323
Offset: 1

Views

Author

G. L. Honaker, Jr.

Keywords

Comments

The next term 729096599629...1413141...926995690927 has 2971 digits. - Metin Sariyar, Jul 07 2020

Links

Crossrefs

Cf. A000796, A007523, A039954.

Programs

  • Mathematica
    l={};Do[a=Floor[Pi*10^n];r=IntegerReverse[a];r2=Floor[r/10];c=FromDigits[Flatten[IntegerDigits/@Join[r2,a]]];
If[PrimeQ[c],AppendTo[l, c]],{n,0,100}];l (* Metin Sariyar, Jul 07 2020 *)

A282183 Numbers k such that the reverse of the first k digits in the decimal expansion of Pi forms a prime.

Original entry on oeis.org

1, 2, 5, 6, 7, 11, 15, 712, 7599, 13280, 13281, 21598, 23233
Offset: 1

Views

Author

XU Pingya, Feb 13 2017

Keywords

Comments

The initial digits of a few corresponding primes are in A007523. The last one a(10)=768556......62951413 is a prime with 13280-digit. That is A092845(13279).
a(14) > 50000. - Michael S. Branicky, Feb 06 2025

Examples

			1 is a term as the first digit of pi, 3, reversed is prime. 2 is a term as the first two digits of pi, 31, reversed is prime. 3 is not a term as the first three digits of pi, 314, reversed, is not prime. - _David A. Corneth_, Feb 13 2017

Links

  • Shyam Sunder Gupta, Mystery of pi, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 19, 473-497.

Crossrefs

Cf. A092845, A007523, A011545.

Programs

  • Mathematica
    Do[If[PrimeQ[FromDigits[Reverse[IntegerDigits[Floor[Pi*10^(n - 1)]]]]],Print[n]],{n, 13335}]
Module[{pid=RealDigits[Pi,10,20000][[1]]},Select[Range[16000],PrimeQ[ FromDigits[ Reverse[Take[pid,#]]]]&]] (* Harvey P. Dale, Sep 06 2019 *)

Extensions

a(11)-a(13) from Michael S. Branicky, Feb 06 2025
Showing 1-3 of 3 results.

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