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 1-9 of 9 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

Views

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

A135697 Palindromes formed from the reflected decimal expansion of Pi.

Original entry on oeis.org

3, 33, 313, 3113, 31413, 314413, 3141413, 31411413, 314151413, 3141551413, 31415951413, 314159951413, 3141592951413, 31415922951413, 314159262951413, 3141592662951413, 31415926562951413, 314159265562951413, 3141592653562951413, 31415926533562951413, 314159265353562951413
Offset: 1

Views

Author

Omar E. Pol, Mar 01 2008, Mar 28 2008

Keywords

Comments

Pi = 3.14159265358979323846264338327... (see A000796).
The number of digits of a(n) is equal to n.

Examples

			   n        Digits of a(n)
   1             ( 3 )
   2            ( 3 3 )
   3           ( 3 1 3 )
   4          ( 3 1 1 3 )
   5         ( 3 1 4 1 3 )
   6        ( 3 1 4 4 1 3 )
   7       ( 3 1 4 1 4 1 3 )
   8      ( 3 1 4 1 1 4 1 3 )
   9     ( 3 1 4 1 5 1 4 1 3 )
  10    ( 3 1 4 1 5 5 1 4 1 3 )
		

Crossrefs

Programs

  • Mathematica
    Table[FromDigits[Join[#[[;; Floor[n/2]]], #[[Ceiling[n/2] ;; 1 ;; -1]]]], {n, Length[#]}] & [First[RealDigits[Pi, 10, 25]]] (* Paolo Xausa, Dec 09 2024 *)

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

Keywords

Comments

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

Crossrefs

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 *)

A135698 Palindromes with odd number of digits formed from the reflected decimal expansion of Pi.

Original entry on oeis.org

3, 313, 31413, 3141413, 314151413, 31415951413, 3141592951413, 314159262951413, 31415926562951413, 3141592653562951413, 314159265353562951413, 31415926535853562951413, 3141592653589853562951413, 314159265358979853562951413, 31415926535897979853562951413
Offset: 1

Views

Author

Omar E. Pol, Mar 01 2008, Mar 28 2008

Keywords

Comments

Pi = 3.14159265358979323846264338327... (see A000796).
The number of digits of a(n) is equal to 2n - 1.
The first five members of this sequence are in the example of A119351.

Examples

			n ........... a(n)
1 ............ 3
2 ........... 313
3 .......... 31413
4 ......... 3141413
5 ........ 314151413
6 ....... 31415951413
7 ...... 3141592951413
8 ..... 314159262951413
9 .... 31415926562951413
10 .. 3141592653562951413
		

Crossrefs

Programs

  • Mathematica
    pinxt[n_]:=With[{pid=RealDigits[Pi,10,20][[1]]},Module[{a=Take[pid,n]}, FromDigits[Join[a,Reverse[Most[a]]]]]]; Table[pinxt[n],{n,1,15}] (* Harvey P. Dale, Oct 06 2011 *)

Extensions

More terms from Harvey P. Dale, Oct 06 2011

A119351 Indices k of prime palindromic numbers formed by taking k digits in the decimal expansion of Pi and reflecting about the last digit.

Original entry on oeis.org

1, 2, 27, 151, 461, 2056
Offset: 1

Views

Author

Eric W. Weisstein, May 15 2006; corrected May 27 2006

Keywords

Comments

The primes corresponding to these indices are A039954.
a(7) > 50000. - Michael S. Branicky, Feb 11 2025

Examples

			Of 3, 313, 31413, 3141413, 314151413, the first and second are primes, so the first two terms are 1 and 2.
		

Crossrefs

Cf. A039954.

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

A383404 Palindromic primes formed from the reflected decimal expansion of the golden ratio phi.

Original entry on oeis.org

11, 1618033308161, 16180339887498948482045868343656381118365634386854028484989478893308161, 16180339887498948482045868343656381177203030277118365634386854028484989478893308161
Offset: 1

Views

Author

Omar E. Pol, May 06 2025

Keywords

Comments

Primes in A135700.
Terms with an odd number of digits are the primes in A135699.

Crossrefs

Showing 1-9 of 9 results.