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 1-7 of 7 results.

A109631 Smallest number m such that n divides (10's complement factorial of m).

Original entry on oeis.org

1, 2, 1, 2, 5, 2, 3, 2, 1, 5, 12, 2, 22, 3, 5, 4, 15, 2, 24, 5, 3, 12, 31, 2, 10, 22, 4, 3, 13, 5, 38, 6, 12, 15, 5, 2, 26, 24, 22, 5, 18, 3, 14, 12, 5, 31, 53, 4, 16, 10, 15, 22, 47, 4, 12, 3, 24, 13, 41, 5, 39, 38, 3, 6, 22, 12, 33, 15, 31, 5, 29, 2, 27, 26
Offset: 1

Views

Author

Jason Earls, Aug 03 2005

Keywords

Comments

Are 374 and 2057 the only n such that a(n) = a(n+1)?

Examples

			a(7)=3 because 7 divides (10-3)*(10-2)*(10-1) and 7 does not divide (10's complement factorial of k) for k < 3.

Links

Crossrefs

Cf. A002034, A109640, A110396.

Programs

  • PARI
    g(p, e) = my(t=0); for(i=logint(p, 10), oo, forstep(j=10^i+(9*10^i)%p, 10^(i+1)-1, p, if(e<=t+=valuation(10^(i+1)-j, p), return(j))));
a(n) = my(m=1); foreach(factor(n)~, f, m=max(m, g(f[1], f[2]))); m; \\ Jinyuan Wang, Aug 09 2025

A109616 Numbers k > 0 such that (10's complement factorial of k) + 1 is prime.

Original entry on oeis.org

2, 5, 10, 25, 36, 44, 65, 67, 138, 149, 176, 212, 279, 1293, 2367, 2463, 2707, 3130, 4150, 4635, 6070, 6355, 10111, 10560
Offset: 1

Views

Author

Jason Earls, Aug 01 2005

Keywords

Comments

Larger values not certified.
Some of the larger entries may only correspond to probable primes.
a(25) > 16000. - Michael S. Branicky, Apr 27 2025

Examples

			5 is a term because (10-5)*(10-4)*(10-3)*(10-2)*(10-1) + 1 = 15121 is prime.
10 is a term because (100-10)*(10-9)*..*(10-1) + 1 = 32659201 is prime.

Crossrefs

Cf. A110396, A109617.

Programs

  • Maple
    b:= proc(n) option remember; `if`(n=0, 1,
      (10^length(n)-n)*b(n-1))
    end:
q:= n-> isprime(1+b(n)):
select(q, [$1..300])[];  # Alois P. Heinz, Aug 13 2025
  • Mathematica
    f[n_] := 10^Length[IntegerDigits[n]] - n; p = 1; Do[p *= f[n]; If[PrimeQ[p + 1], Print[n]], {n, 4635}] (* Ryan Propper, May 20 2006 *)

Extensions

a(14)-a(20) from Ryan Propper, May 20 2006
a(21)-a(24) from Michael S. Branicky, Apr 25 2025

A109617 Numbers k such that (10's complement factorial of k) - 1 is prime.

Original entry on oeis.org

2, 3, 4, 7, 77, 337, 397, 566, 615, 822, 1007, 1017, 1073, 1351, 1731, 2635, 6606, 8513, 10404
Offset: 1

Views

Author

Jason Earls, Aug 01 2005

Keywords

Examples

			3 is a term because (10-3)*(10-2)*(10-1) - 1 = 503 is prime.
77 is a term because (100-77)*..*(100-10)*(10-9)*..*(10-1) - 1 is prime.

Crossrefs

Cf. A109616, A110396.

Extensions

a(9)-a(17) from Jinyuan Wang, Aug 09 2025
a(18)-a(19) from Michael S. Branicky, Aug 13 2025

A109640 Indices of records in A109631.

Original entry on oeis.org

1, 2, 5, 11, 13, 19, 23, 31, 47, 97, 101, 113, 131, 151, 181, 227, 307, 457, 907, 1009, 1129, 1289, 1511, 1801, 2251, 3001, 4507, 9001, 10007, 11251, 12889, 15013, 18013, 22501, 30011, 45007, 90001, 100003, 112501, 128591, 150001, 180001, 225023, 300007, 450001
Offset: 1

Views

Author

Jason Earls, Aug 04 2005

Keywords

Comments

Previous name was: Values of k which are incrementally the largest values of the function: Smallest number m such that k divides (10's complement factorial of m).

Crossrefs

Cf. A002034, A109631, A110396.

Programs

  • Maple
    A089186 := proc(n) 10^max(1,ilog10(n)+1)-n ; end: A110396 := proc(n) mul( A089186(i),i=1..n) ; end: A109631 := proc(n) local a; for a from 1 do if A110396(a) mod n = 0 then RETURN(a) ; fi ; od: end: A109640 := proc(n) option remember ; local nprev,aprev,a ; if n = 1 then RETURN(1); else nprev := A109640(n-1) ; aprev := A109631(nprev) ; for a from nprev+1 do if A109631(a) > aprev then RETURN(a) ; fi ; od; fi ; end: for n from 1 do printf("%d, ",A109640(n)) ; od: # R. J. Mathar, Feb 12 2008

Extensions

More terms from R. J. Mathar, Feb 12 2008
a(23)-a(45) from Jinyuan Wang, Aug 09 2025
New name (using comment from R. J. Mathar) from Joerg Arndt, Aug 09 2025

A109757 Numbers n such that (10's complement factorial of n) + 1 is semiprime.

Original entry on oeis.org

1, 3, 6, 14, 20, 21, 26, 34, 37, 39, 40, 47, 51, 54, 61, 62, 72, 74, 77, 82, 83, 86, 113, 115, 118, 127, 139, 179
Offset: 1

Views

Author

Jason Earls, Aug 12 2005

Keywords

Crossrefs

Cf. A110396, A109616.

Programs

Extensions

More terms from Sean A. Irvine, Jul 10 2011

A109758 Numbers k such that (10's complement factorial of k) - 1 is semiprime.

Original entry on oeis.org

5, 6, 10, 13, 20, 22, 23, 24, 27, 29, 33, 40, 41, 43, 46, 51, 54, 79, 80, 83, 85, 93, 106, 111
Offset: 1

Views

Author

Jason Earls, Aug 12 2005

Keywords

Comments

Sequence possibly continues with 112, 137, 145, 148, 163, 165, 177, 190, 196, 197. 206 is the next certain term. - Tyler Busby, Feb 09 2023

Crossrefs

Cf. A110396, A109617.

Extensions

More terms from Sean A. Irvine, Sep 18 2012

A119384 Ten's complement of the factorials.

Original entry on oeis.org

9, 8, 4, 76, 880, 280, 4960, 59680, 637120, 6371200, 60083200, 520998400, 3772979200, 12821708800, 8692325632000, 79077210112000, 644312571904000, 3597626294272000, 878354899591168000, 7567097991823360000, 48909057828290560000, 8875999272222392320000
Offset: 1

Views

Author

Jason Earls, Jul 24 2006

Keywords

References

  • J. Earls & J. Rogers, 0.1361015212836455566..., Lulu Press, NY, 2006, p. 32.

Links

Crossrefs

Cf. A000142, A110396.

Programs

  • Mathematica
    Table[10^Length[IntegerDigits[n!]]-n!,{n,22}] (* James C. McMahon, Sep 13 2024 *)

Formula

a(n) = 10^length(n!) - n!.

Extensions

a(21)-a(22) from James C. McMahon, Sep 13 2024
Showing 1-7 of 7 results.

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