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.

A007523 Primes in A092845 (decimal expansion of Pi written backwards).

Original entry on oeis.org

3, 13, 51413, 951413, 2951413, 53562951413, 979853562951413
Offset: 1

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Author

Keywords

Comments

Next term is probably A092845(711), a 712-digit probable prime (Baillie-Pomerance-Selfridge-Wagstaff test, cf. PARI/GP documentation) beginning 2116599102453... and ending ...62648323979853562951413.
a(8) = A092845(711) is now a proven prime. - Sean A. Irvine, Jan 07 2018

Examples

			51413 is in the list because it is prime and its decimal reversal, 31415, is the first 5 digits of Pi.
		

References

  • M. Gardner, Whys and Wherefores, Univ. Chicago Press, 1989, p. 84.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

  • Mathematica
    Module[{nn=1000,rd},d=RealDigits[Pi,10,nn][[1]];Select[Table[FromDigits[Reverse[Take[d,n]]],{n,nn}],PrimeQ]]  (* Harvey P. Dale, Jul 11 2023 *)

Formula

Equals A000040 intersect A092845.

Extensions

Edited by M. F. Hasler and N. J. A. Sloane, Mar 30 2008
Edited by T. D. Noe, Oct 30 2008

A371720 a(n) = m^^m mod 10^len(m), where m = A038399(n) and ^^ indicates tetration or hyper-4.

Original entry on oeis.org

1, 11, 811, 3811, 63811, 763811, 3763811, 5103763811, 515103763811, 19515103763811, 6819515103763811, 8146819515103763811, 3808146819515103763811, 7213808146819515103763811, 9807213808146819515103763811, 4939807213808146819515103763811
Offset: 1

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Author

Marco Ripà, Apr 04 2024

Keywords

Comments

For any n, a(n) == a(n + 1) (mod 10^len(A038399(n))), where len(k) := number of digits in k. Assuming len(a(n)) > 1, this is a general property of every concatenated sequence with fixed rightmost digits (such as A014925, A061839, A092845, and A104759), as shown in Ripà's book "La strana coda della serie n^n^...^n".
Moreover, assuming n > 1, since A038399(n) is congruent to 11 (mod 20), the convergence speed of A038399(n)^^b (say, V(A038399(n), b) = {2, 1, 1, 1, ...}) is 2 at height 1 and becomes a unit value for any integer b > 1 (see Links). Hence, a(n) is given by A038399(n)^^len(A038399(n) - 1) (mod 10^len(A038399(n))), and also by A038399(n)^^len(A038399(n)) (mod 10^len(A038399(n))) since A038399(n)^^len(A038399(n)) == A038399(n)^^len(A038399(n) - 1) (mod 10^len(A038399(n))) holds for any n.

Examples

			a(8) is given by the rightmost 10 digits of 2113853211^^2113853211 and thus a(8) = 5103763811.
a(9) == a(8) (mod 10^10), i.e., the digits of a(9) end with the digits of a(8) (and then a(9) has 2 more preceding).
		

References

  • Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6

Crossrefs

Cf. A000045 (Fibonacci), A038399, A171882 (tetration), A317824, A317903, A317905.

Formula

a(n) = A038399(n)^^(len(A038399(n)) - 1) mod 10^len(A038399(n)), where len(A038399(n)) = ceiling(log_10(A038399(n) + 1)).

A254898 Read the first n decimal digits of Pi-3 backwards.

Original entry on oeis.org

1, 41, 141, 5141, 95141, 295141, 6295141, 56295141, 356295141, 5356295141, 85356295141, 985356295141, 7985356295141, 97985356295141, 397985356295141, 2397985356295141, 32397985356295141, 832397985356295141, 4832397985356295141, 64832397985356295141, 264832397985356295141
Offset: 1

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Author

Christian Perfect, Feb 10 2015

Keywords

Comments

a(n) is A039916(n) read backwards.
With the 3 on the end: A092845.

Crossrefs

Programs

  • Mathematica
    Module[{nn=30,pd},pd=Rest[RealDigits[Pi,10,nn][[1]]];Table[FromDigits[ Reverse[ Take[pd,n]]],{n,nn-1}]] (* Harvey P. Dale, Feb 07 2019 *)

Formula

a(n) = A004086(A039916(n)). - Alois P. Heinz, Feb 16 2015

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
		

Crossrefs

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 1-4 of 4 results.