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.

Previous Showing 11-15 of 15 results.

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

Links

Crossrefs

Cf. A065828 up to A065840, A000796, A011545, A011546, A055145, A005042, A060421, A039954, A048796.

A065991 Numbers k such that the first k base-4 digits of Pi expressed in decimal forms a prime.

Original entry on oeis.org

1, 62, 3253, 4490, 62622
Offset: 1

Views

Author

Robert G. Wilson v, Dec 10 2001

Keywords

Comments

a(6) > 10^5. - Michael S. Branicky, Aug 14 2025

Examples

			The first 62 quaternary digits of Pi (A004603) are 30210033312222020201122030020310301030121202202320003130013031 = 16703571626015105435307505830654230989 in decimal, which is a prime.

Crossrefs

Cf. A004603, A060421.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ FromDigits[ First[ RealDigits[Pi, 4, n]], 4]], Print[n]], {n, 1, 4000} ]

Extensions

a(4) from Pontus von Brömssen, Aug 02 2025
a(5) from Michael S. Branicky, Aug 13 2025

A276195 Smallest prime >= decimal expansion of Pi truncated to n places (A011545).

Original entry on oeis.org

3, 31, 317, 3163, 31469, 314159, 3141601, 31415971, 314159311, 3141592661, 31415926541, 314159265359, 3141592653601, 31415926535933, 314159265359057, 3141592653589861, 31415926535897999, 314159265358979347, 3141592653589793239, 31415926535897932429, 314159265358979323861
Offset: 0

Views

Author

Ilya Gutkovskiy, Aug 24 2016

Keywords

Examples

			a(6) = 3141601, since this is the smallest prime >= floor(Pi*10^6) = 3141592.
Pi = 3.1415926535897932384626433832795028841971…

Links

Crossrefs

Cf. A000040, A000720, A000796, A005042, A007918, A011545, A060421.

Programs

  • Mathematica
    Table[NextPrime[Floor[Pi 10^n] - 1], {n, 0, 20}]
Module[{nn=30,pid},pid=RealDigits[Pi,10,nn][[1]];Table[NextPrime[FromDigits[Take[pid,n]]-1],{n,nn}]] (* Harvey P. Dale, Mar 01 2024 *)

Formula

a(n) = A007918(A011545(n)).
a(n) = A000040(A000720(A011545(n)-1)+1).
a(A060421(n)-1) = A005042(n).

A231336 Integers n such that appending some decimal digit to the first n digits of Pi results in a prime.

Original entry on oeis.org

0, 1, 2, 5, 11, 12, 18, 37, 39, 77, 82, 100, 125, 128, 220, 305, 601, 676, 1692, 1901, 2202, 2253, 2394, 3318, 3970, 5826, 7001, 9853, 12607, 13434, 16207
Offset: 1

Views

Author

Marvin Ray Burns and Robert G. Wilson v, Nov 07 2013

Keywords

Comments

A140515 is a proper subsequence. A060421 - 1 is a proper subsequence. So the terms 47576 & 78072 are also members.

Examples

			0 is in the sequence since 2, 3, 5, and 7 are all primes;
1 is in the sequence since 31 and 37 are both primes;
2 is in the sequence since 311, 313, and 317 are all primes;
3 is not in the sequence since 3141, 3143, 3147, and 3149 are all composites;
4 is not in the sequence since 31411, 31413, 31417, and 31419 are all composites;
5 is in the sequence since 314159 is a prime; etc.

Crossrefs

Cf. A140515, A060421, A005042.

Programs

  • Mathematica
    fQ[n_] := Union[PrimeQ[ 10 IntegerPart[10^n*Pi] + {1, 3, 7, 9}]][[-1]]; k = -1; lst = {}; While[k < 17001, If[ fQ@ k, AppendTo[lst, k + 1]; Print[k + 1]]; k++]; lst
Module[{nn=16300,pd},pd=RealDigits[Pi,10,nn][[1]];Select[Range[0,nn],AnyTrue[ 10*FromDigits[Take[pd,#]]+{1,3,7,9},PrimeQ]&]] (* Harvey P. Dale, Aug 14 2022 *)
  • PARI
    is(n)=my(d=Pi*10^n\10*10);isprime(d+1) || isprime(d+3) || isprime(d+7) || isprime(d+9) \\ Charles R Greathouse IV, Nov 07 2013

Extensions

Keyword "base" added by Zak Seidov, Nov 11 2013

A371224 Least prime factor of the integer formed by the first n decimal digits of Pi, or 0 if that number is prime.

Original entry on oeis.org

0, 0, 2, 3, 5, 0, 2, 2, 3, 3, 5, 2, 13, 163, 43, 13, 2, 317213509, 2, 2, 2, 2, 2, 2, 83, 41, 2, 3, 2, 3, 3, 5, 2, 2, 2, 2, 2, 0, 13, 59, 3, 2, 3, 3, 3, 3, 3, 31, 3, 1657, 2, 3, 2, 2, 2, 29, 13, 2, 3, 2, 2, 5, 2828293681646068747, 2, 3, 2, 223, 2, 7
Offset: 1

Views

Author

M. F. Hasler, Mar 15 2024

Keywords

Comments

Complementary to the sequences A005042 (primes in the initial digits of Pi) and A060421 which lists numbers N such that the first N digits of Pi form a prime - exactly the indices of zeros in the present sequence.

Crossrefs

Cf. A000796 (decimals of Pi), A005042 (primes in A011545), A011545 (integer made of n+1 initial digits of Pi), A060421 (length of A005042(n)), A020639 (smallest prime factor of n), A000040 (primes), A089281 (smallest prime factor of A011545(n)).

Programs

  • PARI
    a(n, c=Pi)={ if( n>=precision(c), error("insufficient precision"), !ispseudoprime(c\10^-n--), factor(c\.1^n)[1,1], 0)}

Formula

a(n) = 0 <=> n is in A060421 <=> A011545(n-1) is in A000040 (primes).
a(n) = A089281(n) = A020639(A011545(n-1)) whenever a(n) is nonzero.
a(n) = 2 <=> A000796(2-n) is even <=> A011545(n-1) is even.
Previous Showing 11-15 of 15 results.

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