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 1-4 of 4 results.

A065840 Numbers n such that the first n quaternary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).

Original entry on oeis.org

1, 2, 3, 5, 10, 19, 72, 115, 220, 315, 375, 12408
Offset: 1

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Author

Patrick De Geest, Nov 24 2001

Keywords

Comments

In other words, take the decimal expansion of Pi, drop any digits greater than 4, omit the decimal point and look for prefixes in the resulting string which form base-4 primes.
Numbers n such that A065838(n) is prime.
The next term in the sequence, if it exists, is greater than 10000. - Nathaniel Johnston, Nov 15 2010

Examples

			E.g., the first a(5) or 10 quaternary digits of Pi are 31.12332323{4} and 3112332323{4} is the prime 880571{10}.
		

Crossrefs

Programs

  • Mathematica
    p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]

Extensions

a(12) from Chai Wah Wu, Apr 07 2020

A065832 Numbers k such that the first k binary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).

Original entry on oeis.org

2, 4, 10, 24, 29, 34, 43, 62, 76, 351, 778, 2736, 4992, 7517, 22044, 40390, 204505
Offset: 1

Views

Author

Patrick De Geest, Nov 24 2001

Keywords

Comments

In other words, take the decimal expansion of Pi, drop any digits greater than 1, omit the decimal point and look for prefixes in the resulting string which form base-2 primes.
Numbers k such that A065830(k) is prime.

Examples

			The first a(3)=10 binary digits of Pi are 1101110001_2 which is prime 881_10.
		

Crossrefs

Programs

  • Mathematica
    p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 2]], Print[n]], {n, 1, Length[p] } ]

Extensions

More terms from Robert G. Wilson v, Nov 30 2001
a(15)-a(16) from Chai Wah Wu, Apr 06 2020
a(17) from Michael S. Branicky, Sep 25 2024

A065831 Primes found in A065830.

Original entry on oeis.org

3, 13, 881, 14436001, 461952047, 14782465513, 7568622343067, 3968137871002260679, 65013970878501038966321
Offset: 1

Views

Author

Patrick De Geest, Nov 24 2001

Keywords

Crossrefs

Formula

a(n) = A065830(A065832(n)). - Jinyuan Wang, Aug 31 2021

A065839 Primes found in A065838.

Original entry on oeis.org

3, 13, 53, 859, 880571, 230836658783, 18727694659923768688081143062632211180505377, 1448985191439414787314128433365601157107793684026416650771108564122239
Offset: 1

Views

Author

Patrick De Geest, Nov 24 2001

Keywords

Crossrefs

Showing 1-4 of 4 results.