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.

A125717 a(0)=0; thereafter a(n) = the smallest nonnegative integer not already in the sequence such that a(n-1) is congruent to a(n) (mod n).

Original entry on oeis.org

0, 1, 3, 6, 2, 7, 13, 20, 4, 22, 12, 23, 11, 24, 10, 25, 9, 26, 8, 27, 47, 5, 49, 72, 48, 73, 21, 75, 19, 77, 17, 79, 15, 81, 115, 45, 117, 43, 119, 41, 121, 39, 123, 37, 125, 35, 127, 33, 129, 31, 131, 29, 133, 80, 134, 189, 245, 74, 16, 193, 253, 70, 132, 69, 197, 67, 199, 65
Offset: 0

Views

Author

Leroy Quet, Feb 01 2007

Keywords

Comments

This sequence seems likely to be a permutation of the nonnegative integers.
A245340(n) = smallest m such that a(m) = n, or -1 if n never appears.
See A245394 and A245395 for record values of a(n) and where they occur. - Reinhard Zumkeller, Jul 21 2014
See A370956 and A370959 for record values of the inverse A245340 and where they occur. - N. J. A. Sloane, Apr 29 2024
A very nice (maybe the most natural) variant of Recamán's sequence A005132. - M. F. Hasler, Nov 03 2014

Links

Crossrefs

Cf. A245340 (inverse), A370957 (first differences), A245394 & A245395 (records in this sequence), A370956 & A370959 (records in inverse).
See also A005132 (Recaman), A099506, A125715, A125718, A125725.

Programs

  • Haskell
    import Data.IntMap (singleton, member, (!), insert)
a125717 n = a125717_list !! n
a125717_list =  0 : f [1..] 0 (singleton 0 0) where
   f (v:vs) w m = g (reverse[w-v,w-2*v..1] ++ [w+v,w+2*v..]) where
     g (x:xs) = if x `member` m then g xs else x : f vs x (insert x v m)
-- Reinhard Zumkeller, Jul 21 2014
  • Mathematica
    f[l_List] := Block[{n = Length[l], k = Mod[l[[ -1]], n]},While[MemberQ[l, k], k += n];Append[l, k]];Nest[f, {0}, 70] (* Ray Chandler, Feb 04 2007, updated for change to offset Oct 10 2019 *)
  • PARI
    {Quet_p2(n)=/* Permutation sequence a'la Leroy Quet, A125717 */local(x=[1],k=0,w=1); for(i=2,n,if((k=x[i-1]%i)==0,k=i);while(bittest(w,k-1)>0,k+=i);x=concat(x,k);w+=2^(k-1)); return(x)} \\ Ferenc Adorjan
  • PARI
    A125717(n,show=0)={my(u=1,a);for(n=1,n,a%=n;while(bittest(u,a),a+=n);u+=1<M. F. Hasler, Nov 03 2014
  • Python
    from itertools import count, islice
def agen(): # generator of terms
    an, aset = 0, {0}
    for n in count(1):
        yield an
        an = next(m for m in count(an%n, n) if m not in aset)
        aset.add(an)
print(list(islice(agen(), 70))) # Michael S. Branicky, Jun 07 2023

Extensions

Extended by Ray Chandler, Feb 04 2007
a(0) added by Franklin T. Adams-Watters, Mar 31 2014
Edited by N. J. A. Sloane, Mar 15 2024

A245340 Smallest m such that A125717(m) = n, or -1 if n never appears.

Original entry on oeis.org

0, 1, 4, 2, 8, 21, 3, 5, 18, 16, 14, 12, 10, 6, 1518, 32, 58, 30, 184, 28, 7, 26, 9, 11, 13, 15, 17, 19, 102, 51, 100, 49, 98, 47, 96, 45, 94, 43, 92, 41, 90, 39, 88, 37, 86, 35, 84, 20, 24, 22, 505, 81, 2510, 79, 166, 77, 296, 75, 501, 73, 162, 71, 498, 69
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 21 2014

Keywords

Comments

Conjecture: a(n) is never -1.

Links

Crossrefs

Cf. A245394, A245395, A057167.
For RECORDS see A370956 and A370959.

Programs

  • Haskell
    import Data.IntMap (singleton, member, (!), insert)
a245340 n = a245340_list !! n
a245340_list = 0 : f [1..] [1..] 0 (singleton 0 0) where
   f us'@(u:us) vs'@(v:vs) w m
     | u `member` m = (m ! u) : f us vs' w m
     | otherwise    = g (reverse[w-v,w-2*v..1] ++ [w+v,w+2*v..]) where
     g (x:xs) = if x `member` m then g xs else f us' vs x $ insert x v m
  • Python
    from itertools import count
def A245340(n):
    a, aset = 0, set()
    for m in count(1):
        if a==n: return m-1
        aset.add(a)
        a = next(a for a in count(a%m,m) if a not in aset) # Chai Wah Wu, Mar 13 2024

A370959 Indices of high points in A245340.

Original entry on oeis.org

0, 1, 2, 4, 5, 14, 52, 82, 356, 392, 688, 704, 751, 1325, 1748, 6683, 12570, 24740, 28291, 28307, 45136, 77226, 128419, 135993, 341522, 362992, 643110
Offset: 1

Views

Author

N. J. A. Sloane, Mar 28 2024

Keywords

Crossrefs

The companion to A370956.
Cf. A245340.

Programs

  • Python
    from itertools import count, islice
def A370959_gen(): # generator of terms
    a, aset, b, c = 0, set(), 0, -1
    for n in count(1):
        aset.add(a)
        if a==b:
            if n-1>c:
                c = n-1
                yield a
            while b in aset:
                b += 1
        a = next(a for a in count(a%n,n) if a not in aset)
A370959_list = list(islice(A370959_gen(), 20)) # Chai Wah Wu, Mar 28 2024

Extensions

a(17)-a(23) from Michael S. Branicky, Mar 28 2024
a(24)-a(27) from Chai Wah Wu, Mar 28 2024

A372057 After A125717(n) has been found, a(n) is the smallest missing number.

Original entry on oeis.org

1, 2, 2, 2, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14
Offset: 0

Views

Author

N. J. A. Sloane, Apr 30 2024

Keywords

Crossrefs

Cf. A125717.
A370959 lists the distinct terms in order, and the first differences of A370956 specify the lengths of the runs of identical terms.
Showing 1-4 of 4 results.

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

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