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.

A121538 Increasing sequence: "if n appears then a*n+b doesn't", case a(1)=1, a=2, b=1.

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 10, 11, 12, 14, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 56, 58, 59, 60, 62, 64, 66, 67, 68, 70, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 88, 90, 91, 92, 94, 96, 98, 99, 100
Offset: 1

Views

Author

Zak Seidov, Aug 06 2006

Keywords

Comments

A positive integer n is in A121538 iff any of the following is true: 1) n is even; 2) n+1 = 2^k where k is odd; 3) n+1 = 2^k*(2*t+1) where t>0 and k is even. - Max Alekseyev, Aug 07 2006

Crossrefs

Cf. A121539, A121540, A121541, A121542.

Programs

  • Mathematica
    s={s1=1};With[{a=2,b=1},Do[If[FreeQ[s,(n-b)/a],AppendTo[s,n]],{n,s1+1,100}]];s

Formula

This is essentially A053661-1. - David W. Wilson, Aug 07 2006

A171944 N-positions for game of misere version of Mark.

Original entry on oeis.org

0, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 20, 21, 23, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 63, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99, 100, 101, 103, 105
Offset: 1

Views

Author

N. J. A. Sloane, Oct 29 2010

Keywords

Links

Crossrefs

Complement of A171945. Apart from initial term, same as A053661.

Programs

  • Maple
    A17194X_list := proc(lim, X)
local n, d, S, A;
S := {1}; A := NULL;
for n from 1 to lim do
  d := numtheory[divisors](n);
  if d minus S <> {n} then
     A := A,`if`(X=5,n,iquo(n,2));
     S := S union d;
  fi
od; A end:
# A17194X_list(lim,4) gives A171944_list(lim);
# A17194X_list(lim,5) gives A171945_list(lim).
- Peter Luschny, Dec 28 2010
  • Mathematica
    lim = 210; S = {1}; A = {};
Do[d = Divisors[n]; If[Complement[d, S] != {n}, A = Append[A, Quotient[n, 2]]; S = Union[S, d]], {n, 1, lim}];
A (* Jean-François Alcover, Jul 11 2019, after Peter Luschny *)

A175880 a(1)=1, a(2)=2. If n >= 3: if n/2 is in the sequence, a(n)=0, otherwise a(n)=n.

Original entry on oeis.org

1, 2, 3, 0, 5, 0, 7, 8, 9, 0, 11, 12, 13, 0, 15, 0, 17, 0, 19, 20, 21, 0, 23, 0, 25, 0, 27, 28, 29, 0, 31, 32, 33, 0, 35, 36, 37, 0, 39, 0, 41, 0, 43, 44, 45, 0, 47, 48, 49, 0, 51, 52, 53, 0, 55, 0, 57, 0, 59, 60, 61, 0, 63, 0, 65, 0, 67, 68, 69, 0, 71, 0, 73, 0, 75, 76, 77, 0, 79, 80
Offset: 1

Views

Author

Adriano Caroli, Dec 05 2010

Keywords

Comments

If n > 0 and n is in the sequence, then a(2*n) = 0. Example: 5 is in the sequence, so a(2*5) = a(10) = 0.
Is this a(n) = n*A039982(n-1), n > 1? [R. J. Mathar, Dec 07 2010]

Links

Crossrefs

Cf. A053661.
A000040, A001749, A002001, A002042, A002063, A002089, A003947, A004171 and A081294 are subsequences.

Programs

  • Haskell
    import Data.List (delete)
a175880 n = a175880_list !! (n-1)
a175880_list = 1 : f [2..] [2..] where
   f (x:xs) (y:ys) | x == y    = x : (f xs $ delete (2*x) ys)
                   | otherwise = 0 : (f xs (y:ys))
for_bFile = take 10000 a175880_list
-- Reinhard Zumkeller, Feb 09 2011
  • Maple
    A110654 := proc(n) 2*n+1-(-1)^n ; %/4 ;end proc:
A175880 := proc(n) if n <=2 then n; else if type(n,'even') then n-2*procname(A110654(n)) ; else n; end if; end if; end proc:
seq(A175880(n),n=1..40) ; # R. J. Mathar, Dec 07 2010

Formula

a(n) = n - (1 + (-1)^n) * a((2*n + 1 - (-1)^n)/4), n >= 3.
a(n) = n - A010673(n+1)*a(A110654(n)).

A134623 a(n) = the n-th positive integer which is missing from A134624.

Original entry on oeis.org

2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 20, 21, 23, 25, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 41, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 56, 57, 59, 61, 63, 65, 67, 68, 69, 71, 73, 76, 77, 78, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 100, 101, 102
Offset: 1

Views

Author

Leroy Quet, Nov 04 2007

Keywords

Comments

A134624(1) = 1. A134624(n) is the smallest integer which is > A134624(n-1) and is different from and not coprime to a(n-1). [corrected by Michel Marcus, Sep 06 2019]

Crossrefs

Cf. A053661, A134624.

Programs

  • PARI
    missing(n, v) = {my(nb = 0, k = 1, s = Set(v), ok = 0); while(!ok, if (! setsearch(s, k), nb++); ok = (nb == n); if (!ok, k++);); k;}
nextt(start, cop) = {my(k = max(start+1, cop+1)); while(gcd(k, cop) == 1, k++); k;}
list3(nn) = {my(v3 = vector(nn), v4 = vector(nn)); v4[1] = 1; for (n=1, nn, v3[n] = missing(n, v4); if (n+1 > nn, break); v4[n+1] = nextt(v4[n], v3[n]);); v3} \\ Michel Marcus, Sep 06 2019

Extensions

More terms from Michel Marcus, Sep 06 2019

A274688 First differences of A274687.

Original entry on oeis.org

-2, 3, -5, 7, -8, 9, -11, 12, -13, 15, -17, 19, -20, 21, -23, 25, -27, 28, -29, 31, -32, 33, -35, 36, -37, 39, -41, 43, -44, 45, -47, 48, -49, 51, -52, 53, -55, 57, -59, 60, -61, 63, -65, 67, -68, 69, -71, 73, -75, 76, -77, 79, -80, 81, -83, 84, -85, 87, -89
Offset: 1

Views

Author

Max Barrentine, Jul 02 2016

Keywords

Comments

This sequence and its partial sums plus one list every integer except zero.

Crossrefs

Cf. A030124, A053661, A274687.

Formula

If n is even, a(n) = A053661(n+1); if n is odd, a(n) = -A053661(n+1)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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