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.

A351646 a(n) = A097465(n) - n.

Original entry on oeis.org

0, 1, 2, -2, 2, -2, 2, 3, -3, 3, -3, 3, 4, -4, 4, -4, 6, -4, 6, -4, 0, 4, 6, -6, 6, -6, 0, -6, 6, -6, 6, -4, 0, 4, 6, -6, 6, -6, 0, -6, 4, 5, -7, 5, -5, 5, -3, 5, -7, 5, -5, 5, -3, 5, -7, 5, -5, 5, -1, 5, -7, 5, -7, 5, -3, 5, -7, 5, -5, 5, -3, 5, -1, 5, -9, 7
Offset: 1

Views

Author

Michael De Vlieger, May 05 2022

Keywords

Comments

Zeros correspond to fixed points in A097465, which are listed in A352096.

Links

Crossrefs

Cf. A097465, A352096.

Programs

  • Mathematica
    nn = 2^20; c = {1}; j = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[FreeQ[c, k], CoprimeQ[j, k], k != j + 1, k != j - 1], k++]; j = k; AppendTo[c, k]; Sow[k - i]; If[k == u, While[MemberQ[c, u], u++]; c = DeleteCases[c, _?(# < u &)]], {i, 2, nn}]][[-1, -1]]

A352096 Fixed points in A097465.

Original entry on oeis.org

1, 21, 27, 33, 39, 297, 429, 478, 495, 501, 2138, 3854, 4712, 6428, 8144, 9711, 21872, 37791, 57052, 80216, 88179, 89654, 94802, 109388, 113373, 163761, 171166, 182318, 188955, 196904, 203768, 211490, 214149, 239343, 1805247, 1820092, 1849821, 1983543, 2072691
Offset: 1

Views

Author

Michael De Vlieger, May 05 2022

Keywords

Comments

Position of zeros in A351646.
Analogous to A352931 regarding A093714.

Crossrefs

Cf. A093714, A097465, A351646, A352931, A353069.

Programs

  • Mathematica
    nn = 2^20; c = {1}; j = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[FreeQ[c, k], CoprimeQ[j, k], k != j + 1, k != j - 1], k++]; j = k; AppendTo[c, k]; If[k == i, Sow[k]]; If[k == u, While[MemberQ[c, u], u++]; c = DeleteCases[c, _?(# < u &)]], {i, 2, nn}]][[-1, -1]]

A353069 Positions k such that A097465(k) and A097465(k+1) are odd.

Original entry on oeis.org

1, 2, 7, 12, 41, 100, 521, 1150, 10391, 15008, 255247, 1786778, 4849835, 5870858, 6561553, 557732162, 3234846601, 3457939474, 4360010651
Offset: 1

Views

Author

Michael De Vlieger, May 05 2022

Keywords

Comments

Fixed points in A097465 appear in the intervals [12, 41], [100, 521], [1150, 10391], etc.

Links

Crossrefs

Cf. A097465, A351646, A352096.

Programs

  • C
    See Links section.
  • Mathematica
    nn = 2^20; c = {1}; j = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[FreeQ[c, k], CoprimeQ[j, k], k != j + 1, k != j - 1], k++]; j = k; AppendTo[c, k]; If[# != s, s = #; Sow[i - 1]] &@ Mod[#, 2] &@ Abs[k - i]; If[k == u, While[MemberQ[c, u], u++]; c = DeleteCases[c, _?(# < u &)]], {i, 2, nn}]][[-1, -1]]

Extensions

a(17)-a(19) from Rémy Sigrist, May 07 2022

A353711 Smallest missing number when A097465(n) is being calculated.

Original entry on oeis.org

1, 2, 2, 2, 4, 4, 6, 6, 6, 8, 8, 10, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 18, 18, 20, 20, 22, 22, 24, 24, 28, 28, 30, 30, 30, 30, 32, 32, 34, 34, 36, 36, 36, 40, 40, 42, 42, 42, 42, 46, 46, 48, 48, 48, 48, 52, 52, 54, 54, 54, 54, 56, 56, 60, 60, 60, 60, 64, 64, 66, 66, 66, 66
Offset: 1

Views

Author

N. J. A. Sloane, May 06 2022

Keywords

Links

Crossrefs

Cf. A097465.

Programs

  • PARI
    See Links section.

A097467 Permutation of natural numbers inverse to A097465.

Original entry on oeis.org

1, 4, 2, 6, 3, 9, 5, 11, 7, 14, 8, 16, 10, 18, 12, 20, 13, 24, 15, 26, 21, 28, 17, 30, 19, 22, 27, 32, 23, 36, 25, 38, 33, 40, 29, 43, 31, 34, 39, 45, 35, 49, 37, 47, 41, 51, 42, 55, 44, 53, 46, 57, 48, 61, 50, 63, 52, 59, 54, 67, 56, 65, 58, 69, 60, 75, 62, 71, 64, 77, 66, 73
Offset: 1

Views

Author

Alec Mihailovs (alec(AT)mihailovs.com), Aug 23 2004

Keywords

Examples

			a(3)=2 because A097465(2)=3.

Crossrefs

Cf. A097465.

Programs

  • Maple
    A:=proc(n) option remember; local t, S; S:=({$1..1000} minus {seq(A(i),i=1..n-1)}) minus {A(n-1)-1,A(n-1)+1}; t:=min(S[]); while igcd(A(n-1),t)>1 do S:=S minus {t}; t:=min(S[]) od; t end: A(1):=1: L:=[seq(A(n),n=1..200)]: a:=n-> if member(n,L,'p') then p else 0 fi: seq(a(n),n=1..195);
Showing 1-5 of 5 results.

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

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