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.

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A231881 The digits of a(n) and a(n+1) together can be reordered to form a square; lexicographically earliest sequence of distinct positive integers with this property.

Original entry on oeis.org

1, 6, 3, 16, 9, 4, 14, 8, 29, 5, 2, 11, 25, 12, 15, 21, 37, 69, 13, 27, 19, 26, 10, 24, 30, 42, 39, 52, 20, 34, 18, 28, 81, 43, 36, 31, 48, 7, 56, 47, 61, 33, 46, 17, 23, 40, 32, 49, 60, 57, 22, 45, 63, 54, 67, 41, 38, 44, 62, 55, 126, 58, 108, 76, 50, 92, 35, 64
Offset: 0

Views

Author

N. J. A. Sloane, Nov 17 2013, based on a posting to the Sequence Fans Mailing List by Andrew Weimholt, Nov 12 2013

Keywords

Comments

A231880 and A231881 eventually merge: A231881(2539) = 2541; A231880(2540) = 2536; A231881(2540,2541,..) = A231880(2541,2542,..) = 2544,2551,.. Hans Havermann, Nov 17 2013

Links

Crossrefs

A variant of A228407. Cf. A231880.

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits@ a[n - 1], t = a@# & /@ Range[0, n - 1]}, Label[start]; While[ MemberQ[t, k], k++]; While[ Select[ Permutations[ Join[idm, IntegerDigits[ k]]], #[[1]] != 0 && IntegerQ[ Sqrt[ FromDigits[ #]]] &] == {}, k++; Goto[start]]; k]; Array[a, 100, 0] (* Robert G. Wilson v, Nov 17 2013 *)

Extensions

Corrected and extended by Hans Havermann, Nov 17 2013

A231921 Terms of A231920 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 4, 1, 3, 9, 5, 2, 6, 10, 8, 12, 20, 24, 27, 11, 7, 13, 17, 23, 25, 28, 14, 16, 18, 22, 26, 29, 15, 19, 21, 31, 35, 37, 39, 47, 51, 59, 61, 65, 69, 73, 75, 81, 30, 36, 40, 44, 50, 52, 56, 60, 68, 70, 72, 76, 80, 82, 32, 34, 38, 42, 46, 48, 54, 58, 62, 64, 66, 74, 78
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

See A231920 for precise definition.
This is a permutation of the nonnegative integers - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230892, A231923, A231925, A231927, A231929, A231931, A231933, A228407, A231920.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 3], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 3]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 100, 0]

A231922 Working in base 4: a(0)=0, thereafter a(n+1) is the smallest number not already in the sequence such that the bits of a(n) and a(n+1) together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 11, 1, 10, 100, 12, 2, 20, 101, 22, 3, 13, 31, 103, 30, 110, 33, 111, 21, 102, 120, 201, 210, 1000, 122, 133, 212, 221, 313, 331, 1001, 112, 23, 32, 113, 131, 223, 232, 300, 311, 322, 333, 1003, 123, 132, 213, 231, 312, 321, 1002, 121, 200, 211, 222, 233, 323, 332
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

This is a permutation of the nonnegative integers in base 4 - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230891, A231920, A231924, A231926, A231928, A231930, A231932, A228407, A231923.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 4], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 4]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 4]

A231923 Terms of A231922 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 5, 1, 4, 16, 6, 2, 8, 17, 10, 3, 7, 13, 19, 12, 20, 15, 21, 9, 18, 24, 33, 36, 64, 26, 31, 38, 41, 55, 61, 65, 22, 11, 14, 23, 29, 43, 46, 48, 53, 58, 63, 67, 27, 30, 39, 45, 54, 57, 66, 25, 32, 37, 42, 47, 59, 62, 68, 34, 40, 51, 60, 69, 28, 49, 52, 71, 35, 44, 50
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

See A231922 for precise definition.
This is a permutation of the nonnegative integers - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230892, A231921, A231925, A231927, A231929, A231931, A231933, A228407, A231922.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 4], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 4]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]

A231924 Working in base 5: a(0)=0, thereafter a(n+1) is the smallest number not already in the sequence such that the bits of a(n) and a(n+1) together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 11, 1, 10, 100, 12, 2, 20, 101, 22, 3, 13, 31, 103, 30, 110, 33, 4, 14, 41, 104, 40, 114, 24, 42, 112, 21, 102, 120, 201, 210, 1000, 111, 44, 113, 23, 32, 121, 200, 211, 222, 233, 244, 323, 332, 424, 442, 1001, 122, 133, 144, 212, 221, 313, 331, 414, 441, 1002, 123
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

This is a permutation of the nonnegative integers in base 5 - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230891, A231920, A231922, A231926, A231928, A231930, A231932, A228407, A231925.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 5], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 5]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 5]

A231925 Terms of A231924 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 6, 1, 5, 25, 7, 2, 10, 26, 12, 3, 8, 16, 28, 15, 30, 18, 4, 9, 21, 29, 20, 34, 14, 22, 32, 11, 27, 35, 51, 55, 125, 31, 24, 33, 13, 17, 36, 50, 56, 62, 68, 74, 88, 92, 114, 122, 126, 37, 43, 49, 57, 61, 83, 91, 109, 121, 127, 38, 42, 58, 66, 82, 86, 128, 40, 76, 80
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

See A231924 for precise definition.
This is a permutation of the nonnegative integers - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230892, A231921, A231923, A231927, A231929, A231931, A231933, A228407, A231924.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 5], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 5]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]

A231926 Working in base 6: a(0)=0, thereafter a(n+1) is the smallest number not already in the sequence such that the bits of a(n) and a(n+1) together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 11, 1, 10, 100, 12, 2, 20, 101, 22, 3, 13, 31, 103, 30, 110, 33, 4, 14, 41, 104, 40, 114, 24, 42, 112, 21, 102, 120, 201, 210, 1000, 105, 15, 5, 25, 52, 115, 35, 53, 113, 23, 32, 121, 44, 55, 111, 51, 122, 133, 144, 155, 212, 221, 313, 331, 414, 441, 515, 551, 1001
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

This is a permutation of the nonnegative integers in base 6 - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230891, A231920, A231922, A231924, A231928, A231930, A231932, A228407, A231927.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 6], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 6]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 6]

A231927 Terms of A231926 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 7, 1, 6, 36, 8, 2, 12, 37, 14, 3, 9, 19, 39, 18, 42, 21, 4, 10, 25, 40, 24, 46, 16, 26, 44, 13, 38, 48, 73, 78, 216, 41, 11, 5, 17, 32, 47, 23, 33, 45, 15, 20, 49, 28, 35, 43, 31, 50, 57, 64, 71, 80, 85, 117, 127, 154, 169, 191, 211, 217, 55, 22, 27, 58, 63, 118, 133
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

See A231926 for precise definition.
This is a permutation of the nonnegative integers - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230892, A231921, A231923, A231925, A231929, A231931, A231933, A228407, A231926.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 6], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 6]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]

A231928 Working in base 7: a(0)=0, thereafter a(n+1) is the smallest number not already in the sequence such that the bits of a(n) and a(n+1) together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 11, 1, 10, 100, 12, 2, 20, 101, 22, 3, 13, 31, 103, 30, 110, 33, 4, 14, 41, 104, 40, 114, 24, 42, 112, 21, 102, 120, 201, 210, 1000, 105, 15, 5, 25, 52, 115, 35, 53, 113, 23, 32, 121, 26, 6, 16, 61, 106, 60, 116, 36, 63, 131, 34, 43, 134, 143, 314, 341, 413, 431, 1003
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

This is a permutation of the nonnegative integers in base 7 - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230891, A231920, A231922, A231924, A231926, A231930, A231932, A228407, A231929.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 7], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 7]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]; FromDigits@# & /@ IntegerDigits[s, 7]

A231929 Terms of A231928 written in base 10: the binary expansions of a(n) and a(n+1) taken together can be rearranged to form a palindrome.

Original entry on oeis.org

0, 8, 1, 7, 49, 9, 2, 14, 50, 16, 3, 10, 22, 52, 21, 56, 24, 4, 11, 29, 53, 28, 60, 18, 30, 58, 15, 51, 63, 99, 105, 343, 54, 12, 5, 19, 37, 61, 26, 38, 59, 17, 23, 64, 20, 6, 13, 43, 55, 42, 62, 27, 45, 71, 25, 31, 74, 80, 158, 176, 206, 218, 346, 57, 32, 40, 48, 65, 36
Offset: 0

Views

Author

N. J. A. Sloane and Robert G. Wilson v, Nov 15 2013

Keywords

Comments

See A231928 for precise definition.
This is a permutation of the nonnegative integers - see the Comments in A228407 for the proof.

Crossrefs

Cf. A230892, A231921, A231923, A231925, A231927, A231931, A231933, A228407, A231928.

Programs

  • Mathematica
    a[0] = 0; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits[ a[n - 1], 7], t = a@# & /@ Range[n - 1]}, Label[ start]; While[ MemberQ[t, k], k++];  While[ Select[ Permutations[ Join[ idm, IntegerDigits[k, 7]]], #[[1]] != 0 && # == Reverse@# &] == {}, k++; Goto[ start]]; k]; s = Array[a, 60, 0]
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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