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 1-5 of 5 results.

A212636 Minimal m >= 1 such that floor((2*n - 1)!!/m) - 2 is prime.

Original entry on oeis.org

1, 1, 3, 3, 8, 1, 1, 1, 5, 7, 19, 7, 5, 15, 7, 17, 5, 3, 9, 11, 63, 9, 5, 1, 53, 27, 51, 11, 3, 11, 13, 15, 17, 35, 1, 17, 21, 13, 139, 61, 3, 13, 1, 7, 147, 23, 123, 47, 41, 35, 11, 39, 69, 21, 123, 29, 27, 49, 3, 9, 37, 171, 57, 1, 31, 37, 5, 61, 27, 31, 53
Offset: 3

Views

Author

Vladimir Shevelev, Feb 14 2013

Keywords

Examples

			(2*6-1)!! = 11!! = 11 * 9 * 7 * 5 * 3 * 1 = 10395. Floor(10395/1) - 2 = 10395 - 2 = 10393 =  19 * 547 is not prime, and floor(10395/2) - 2 = 5197 - 2 = 5195 = 5 * 1039 is not prime, but floor(10395/3) - 2 = 3465 - 2 = 3463 is prime, so a(6) = 3.

Crossrefs

Cf. A212281, A212282, A212321.

Programs

  • Maple
    a:= proc(n) local m;
      for m while not isprime(iquo(doublefactorial(2*n-1), m)-2)
      do od; m
    end:
seq(a(n), n=3..70);  #  Alois P. Heinz, Feb 18 2013
  • Mathematica
    a[n_] := Module[{m}, For[m = 1, True, m++, If[PrimeQ[Floor[(2n-1)!!/m]-2], Return[m]]]];
Table[a[n], {n, 3, 73}] (* Jean-François Alcover, May 24 2025 *)

Extensions

More terms from Alois P. Heinz, Feb 18 2013

A212637 Minimal m>=0 such that (2*n-1)!! + 2^m is prime.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 4, 3, 2, 6, 1, 1, 3, 1, 2, 7, 5, 11, 16, 2, 3, 2, 4, 4, 11, 6, 4, 33, 1, 12, 18, 3, 20, 5, 38, 17, 2, 1, 18, 3, 14, 26, 11, 14, 63, 3, 2, 13, 110, 44, 34, 1, 22, 44, 114, 37, 43, 39, 5, 13, 12, 57, 41, 12, 18, 13, 9, 8, 13, 52, 26, 78, 37, 14
Offset: 1

Views

Author

Vladimir Shevelev, Feb 14 2013

Keywords

Crossrefs

Cf. A212281, A212282, A212321, A212636.

Programs

  • Maple
    a:= proc(n) local m;
      for m from 0 while not isprime(doublefactorial(2*n-1)+2^m)
      do od; m
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Feb 18 2013
  • Mathematica
    a[n_] := Block[{f = (2*n - 1)!!, m = 0}, While[! PrimeQ[f + 2^m], m++]; m]; a/@Range[70] (* Giovanni Resta, Feb 15 2013 *)

Extensions

a(9)-a(70) from Giovanni Resta, Feb 15 2013

A212648 Minimal m >= 0 such that (2*n-1)!! - 2^m is prime.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 1, 1, 1, 6, 9, 2, 6, 6, 8, 16, 2, 15, 6, 3, 3, 5, 7, 26, 1, 8, 16, 18, 7, 14, 12, 9, 5, 14, 8, 1, 32, 7, 2, 2, 3, 53, 8, 1, 3, 10, 10, 20, 8, 25, 20, 2, 23, 7, 13, 21, 87, 16, 76, 35, 30, 18, 12, 7, 1, 117, 36, 40, 57, 25, 3, 5, 47, 62
Offset: 2

Views

Author

Vladimir Shevelev, Feb 14 2013

Keywords

Links

Crossrefs

Cf. A212281, A212282, A212321, A212636, A212637.

Programs

  • Maple
    f:= proc(n) local m,t;
  t:= doublefactorial(2*n-1);
  for m from 0 do
    if isprime(t - 2^m) then return m fi
  od
end proc:
map(f, [$2..100]); # Robert Israel, Jul 20 2023
  • Mathematica
    a[n_] := Block[{f=(2*n-1)!!, m=0}, While[! PrimeQ[f - 2^m], m++]; m]; a /@ Range[2, 75] (* Giovanni Resta, Feb 14 2013 *)

Extensions

a(8)-a(75) from Giovanni Resta, Feb 14 2013

A213366 Minimal of max(m,k) (m>=1,k>=0) such that (2*n-1)!!/m-2^k is prime.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 1, 1, 1, 5, 3, 2, 6, 5, 3, 5, 2, 3, 3, 3, 3, 5, 5, 3, 1, 7, 5, 8, 7, 3, 5, 5, 5, 5, 7, 1, 9, 7, 2, 2, 3, 3, 7, 1, 3, 10, 7, 5, 4, 11, 9, 2, 9, 7, 9, 9, 13, 13, 9, 3, 9, 5, 12, 7, 1, 5, 7, 5, 9, 6, 3, 5, 5, 11, 10, 1, 5, 5, 7, 3, 3, 3, 8, 9, 2, 6, 7, 4, 7, 9, 5, 4, 6, 7, 5, 10, 15, 4, 9, 11, 15, 9, 21, 13, 7, 11, 7, 8, 7, 8, 12, 7, 4, 12, 5, 7, 20, 9, 5, 21, 2, 1, 3, 9, 5, 13, 16, 13, 9, 4, 15, 11, 13, 5, 2, 9, 7, 11, 11, 11, 17, 9, 8, 9, 15, 15, 2, 12, 3
Offset: 2

Views

Author

Vladimir Shevelev, Feb 15 2013

Keywords

Crossrefs

Cf. A212281, A212282, A212321, A212636, A212637, A212648.

Programs

  • PARI
    a(n)=my(m=-1, P=prod(i=2, n, 2*i-1)); while(m+=2, for(k=m-2, m-1, forstep(M=1, m-2, 2, if(ispseudoprime(P/M-2^k), return(k)))); for(k=0, m, if(ispseudoprime(P/m-2^k), return(m)))) \\ Charles R Greathouse IV, Feb 27 2013

Extensions

Terms beginning with a(10) from Peter J. C. Moses

A213512 Minimal of max(m,k) (m>=1,k>=0) such that (2*n-1)!!/m+2^k is prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 3, 2, 3, 1, 1, 3, 1, 2, 4, 5, 5, 5, 2, 3, 2, 4, 4, 7, 5, 4, 7, 1, 9, 6, 3, 6, 5, 13, 10, 2, 1, 7, 3, 6, 5, 5, 5, 9, 3, 2, 5, 9, 7, 11, 1, 3, 5, 10, 5, 7, 3, 3, 5, 9, 4, 5, 11, 8, 5, 9, 8, 11, 9, 9, 13, 9, 11, 11, 9, 5, 3, 11, 11, 3, 7, 3, 9, 1, 10, 7, 9, 3, 7, 7, 11, 9, 6, 9, 16, 5, 6, 9, 5, 9, 15, 11, 12, 3, 19, 7, 7, 3, 1, 19, 7, 9, 11, 4, 19, 5, 9, 7, 11, 13, 11, 1, 7, 15, 7, 15, 18, 11, 7, 5, 19, 15, 12, 7, 19, 14, 9, 7, 11, 3, 13, 10, 13, 16, 11, 9, 11, 7, 3
Offset: 1

Views

Author

Vladimir Shevelev, Feb 15 2013

Keywords

Crossrefs

Cf. A212281, A212282, A212321, A212636, A212637, A212648, A213366.

Programs

  • PARI
    a(n)=my(m=-1,P=prod(i=2,n,2*i-1)); while(m+=2, for(k=m-2,m-1, forstep(M=1,m-2,2, if(ispseudoprime(P/M+2^k),return(k)))); for(k=0,m, if(ispseudoprime(P/m+2^k),return(m)))) \\ Charles R Greathouse IV, Feb 27 2013

Extensions

Terms beginning with a(6) were calculated by Peter J. C. Moses.
Showing 1-5 of 5 results.

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