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.

A358874 Inverse permutation to A076034.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 12, 16, 8, 22, 9, 29, 30, 37, 10, 46, 13, 56, 17, 67, 14, 79, 15, 92, 38, 106, 18, 121, 19, 137, 57, 154, 23, 172, 20, 191, 68, 211, 21, 232, 24, 254, 93, 277, 25, 301, 39, 326, 107, 352, 26, 379, 40, 407, 138, 436, 27, 466, 28, 497
Offset: 1

Views

Author

Rémy Sigrist, Dec 04 2022

Keywords

Examples

			A076034(42) = 101, so a(101) = 42.

Links

Crossrefs

Cf. A000124, A076034.

Programs

  • Maple
    S:=[$1..10000]:
V:= Vector(10000): ok:= true;
for n from 1 while ok do
  A:= [S[1]]; R:= 1; count:= 1;
  for k from 2 while count < n do
    if k > nops(S) then ok:= false; break fi;
    if andmap(t -> igcd(t,S[k])=1, A) then count:= count+1; A:= [op(A),S[k]]; R:= R,k; fi
  od;
  S:= subsop(op(map(t -> t=NULL, [R])),S);
  for i from 1 to nops(A) do
    V[A[i]]:= n*(n-1)/2+i
  od
od:
if member(0,V,'q') then convert(V[1..q-1],list)
else convert(V,list)
fi; # Robert Israel, Dec 04 2022
  • PARI
    See Links section.

Formula

a(2*n) = A000124(n).
a(p) < a(n) if p < n with p a prime number.

A076033 Final members of groups in A076034.

Original entry on oeis.org

1, 3, 7, 17, 25, 41, 61, 89, 109, 151, 193, 239, 281, 349, 409, 479, 557, 619, 709, 811, 907, 1013, 1109, 1229, 1327, 1481, 1601, 1741, 1889, 2063, 2221, 2381, 2551, 2729, 2917, 3137, 3331, 3539, 3733, 3943, 4177, 4441, 4663, 4937, 5171, 5437, 5683, 5923
Offset: 1

Views

Author

Amarnath Murthy, Oct 01 2002

Keywords

Crossrefs

Cf. A076032, A076034.

Extensions

More terms from David Wasserman, Jan 29 2005

A358875 Regular table of distinct nonnegative integers built by greedy algorithm such the binary expansions of two distinct terms in the same row have no common 1's.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 5, 10, 16, 32, 6, 9, 48, 64, 128, 7, 24, 96, 256, 512, 1024, 11, 20, 160, 320, 1536, 2048, 4096, 12, 17, 34, 192, 768, 3072, 8192, 16384, 13, 18, 224, 1280, 2560, 12288, 32768, 65536, 131072, 14, 33, 80, 384, 3584, 20480, 40960, 196608, 262144, 524288
Offset: 1

Views

Author

Rémy Sigrist, Dec 04 2022

Keywords

Comments

This sequence is a variant of A076034, and is a bijection from the positive integers to the nonnegative integers (with inverse A358876).
Powers of 2 appear in natural order.

Examples

			Table begins:
    0,
    1, 2,
    3, 4, 8,
    5, 10, 16, 32,
    6, 9, 48, 64, 128,
    7, 24, 96, 256, 512, 1024,
    11, 20, 160, 320, 1536, 2048, 4096,
    12, 17, 34, 192, 768, 3072, 8192, 16384,
    13, 18, 224, 1280, 2560, 12288, 32768, 65536, 131072,
    ...

Links

Crossrefs

Cf. A076034, A358876 (inverse).

Programs

  • PARI
    See Links section.

A385661 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of pairwise coprime integers, the n-th such run having a(n) terms.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 8, 9, 19, 23, 25, 10, 21, 29, 31, 37, 41, 43, 12, 35, 47, 53, 59, 61, 14, 15, 67, 71, 73, 79, 83, 89, 97, 101, 103, 16, 27, 49, 55, 107, 109, 113, 127, 131, 137, 139, 149, 151, 18, 65, 77, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229
Offset: 1

Views

Author

Rémy Sigrist, Aug 09 2025

Keywords

Comments

This sequence is a permutation of the positive integers as each run starts with the least integer not yet in the sequence.
The prime numbers appear in natural order.

Examples

			The first terms and runs are:
  n   a(n)  n-th run
  --  ----  -----------------------------------------------------------
   0     1  1
   1     2  2, 3
   3     3  4, 5, 7
   6     4  6, 11, 13, 17
  10     5  8, 9, 19, 23, 25
  15     7  10, 21, 29, 31, 37, 41, 43
  22     6  12, 35, 47, 53, 59, 61
  28    11  14, 15, 67, 71, 73, 79, 83, 89, 97, 101, 103
  39    13  16, 27, 49, 55, 107, 109, 113, 127, 131, 137, 139, 149, 151

Links

Crossrefs

See A386932 for a similar sequence.
Cf. A076034, A385735 (inverse).

Programs

  • PARI
    \\ See Links section.

Formula

T(n, 1) = 2*n-2 for any n > 1.
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.