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.

A078155 A078152(n!).

Original entry on oeis.org

0, 0, 0, 0, 4, 22, 80, 304, 1043, 3538, 12094, 42979, 156237, 587926, 2283038, 9142910, 37708601, 160014979, 697523776, 3119511496, 14295524835, 67052144163, 321571055089, 1575370699764, 7876854373196, 40164235356266, 208699490940770
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Links

Crossrefs

Cf. A078152, A078153, A078154, A078156, A078157, A078158.

Programs

  • Mathematica
    Table[ Length[ Union[ Table[ Floor[w!/j], {j, 1, w!}]]] - DivisorSigma[0, w! ], {w, 1, 11}]
(* Second program: *)
Array[Floor@ Sqrt[4 # + 1] - 1 - DivisorSigma[0, #] &[#!] &, 27] (* Michael De Vlieger, Dec 13 2018 *)

Formula

a(n) = A078152(n!) = A055086(n!) - A000005(n!).

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
a(11) corrected and terms a(12) onward added by Max Alekseyev, Feb 12 2012

A078156 A078153(n!).

Original entry on oeis.org

0, 0, 0, 0, 46, 702, 7479, 97902, 1231886, 15977798, 208298944, 3085485116, 45879947392, 749485746579, 12963973882204, 236404256556347, 4415737043058504, 88721524940832020, 1830113429944169943, 40228564066847381090, 921832573196324390682
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A078152, A078153, A078154, A078155, A078156, A078157, A078158.

Programs

  • Mathematica
    Table[Length[Union[Table[Floor[w!/j], {j, 1, w!}]]] -DivisorSigma[1, w! ], {w, 1, 9}]

Formula

a(n) = A078153(n!) = A078162(n) - A062569(n)

Extensions

Terms a(10) onward from Max Alekseyev, Feb 12 2012

A078190 Primes of the form A004154(n) - 1.

Original entry on oeis.org

5, 23, 11, 71, 503, 62270207, 871782911, 121645100408831, 243290200817663, 304888344611713860501503, 137637530912263450463159795815809023
Offset: 1

Views

Author

Cino Hilliard, Dec 23 2002

Keywords

Comments

More precisely, scan A004154, subtract 1 and record the answer if it is a prime. The sequence is not monotonic.

Links

Crossrefs

Cf. A004154, A078154, A078203, A078305.

Programs

  • Maple
    A004154 := proc(n) option remember ; local m ; if n <= 1 then RETURN(1) ; else m := A004154(n-1)*n ; while m mod 10 = 0 do m := m /10 ; end ; RETURN(m) ; fi ; end: n := 1 ; while true do f := A004154(n) : if isprime(f-1) then printf("%d, ",f-1) ; fi ; n := n+1 : od : # R. J. Mathar, Feb 27 2007
  • PARI
    v=[];for(n=1,500,if(ispseudoprime(t=n!/10^valuation(n!,5)-1),v=concat(v,t))); v \\ Charles R Greathouse IV, Feb 14 2011

Extensions

More terms from R. J. Mathar, Feb 27 2007

A078203 Numbers k such that A004154(k) + 1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 14, 15, 24, 74, 191, 222, 276, 2200, 3041, 3701, 4324, 6201
Offset: 1

Views

Author

Cino Hilliard, Dec 23 2002

Keywords

Crossrefs

Cf. A004154, A078154, A078190, A078305.

Programs

  • Mathematica
    f[n_] := n!/10^Sum[ Floor[n/5^k], {k, 1, Log[10, n] + 1}]; Do[ If[ PrimeQ[ f[n] + 1], Print[n]], {n, 1, 850}]

Extensions

Extended by Joshua Zucker, Robert G. Wilson v and Jason Earls, Dec 24 2002
a(13) from Don Reble, Jan 12 2006
a(14)-a(17) from Michael S. Branicky, Jul 23 2023

A078305 Numbers k such that A004154(k) - 1 is prime.

Original entry on oeis.org

3, 4, 5, 6, 7, 13, 14, 19, 20, 28, 37, 99, 100, 108, 141, 304, 442, 682, 3641, 4076
Offset: 1

Views

Author

Cino Hilliard, Dec 23 2002

Keywords

Comments

Some of the larger entries may only correspond to probable primes.

Crossrefs

Cf. A004154, A078154, A078203, A078190.

Programs

  • Mathematica
    f[n_] := n!/10^Sum[ Floor[n/5^k], {k, 1, Log[10, n] + 1}]; Do[ If[ PrimeQ[ f[n] - 1], Print[n]], {n, 1, 750}]

Extensions

Extended by Robert G. Wilson v and Jason Earls, Dec 24 2002
a(19)-a(20) from Michael S. Branicky, Jul 23 2023

A078157 a(n) = A078152(2^n).

Original entry on oeis.org

0, 0, 0, 2, 4, 8, 13, 22, 34, 52, 77, 114, 166, 240, 345, 494, 705, 1004, 1427, 2026, 2873, 4072, 5767, 8166, 11558, 16356, 23141, 32738, 46309, 65504, 92648, 131038, 185328, 262108, 370690, 524250, 741416, 1048536, 1482869, 2097110, 2965777
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A078152, A078153, A078154, A078155, A078156, A078158.

Formula

For n>1, a(n) = floor(sqrt(2^(n+2))) - n - 2

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
More terms from Max Alekseyev, Feb 12 2012

A078158 a(n) = A078153(2^n).

Original entry on oeis.org

0, 0, 0, 8, 24, 73, 183, 470, 1112, 2592, 5876, 13233, 29316, 64329, 140028, 302824, 651101, 1393204, 2968129, 6300084, 13326815, 28108564, 59123162, 124065274, 259759346, 542781169, 1132075405, 2357197804, 4900443545, 10173068455, 21090365684
Offset: 1

Views

Author

Labos Elemer, Nov 27 2002

Keywords

Crossrefs

Cf. A078152, A078153, A078154, A078155, A078156, A078157.

Programs

  • Mathematica
    Table[ Apply[ Plus, Union[ Table[ Floor[2^w/j], {j, 1, 2^w}]]] - DivisorSigma[1, 2^w], {w, 1, 24}]

Extensions

Extended by Robert G. Wilson v, Dec 02 2002
Terms a(26) onward from Max Alekseyev, Feb 12 2012
Showing 1-7 of 7 results.

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