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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A256299 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 0 to the digits of n written in base 9, then convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 0, 19, 20, 21, 22, 23, 24, 25, 26, 18, 28, 29, 30, 31, 32, 33, 34, 35, 27, 37, 38, 39, 40, 41, 42, 43, 44, 36, 46, 47, 48, 49, 50, 51, 52, 53, 45, 55, 56, 57, 58, 59, 60, 61, 62, 54, 64, 65, 66, 67, 68, 69
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 9 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256298 for bases 3 through 8, and A256289 for the variant where the result is not converted back to base 10.

Examples

			a(9) = 19 because 9 = 10[9] becomes 21[9] = 19.
a(80) = 0 because 80 = 88[9] becomes 00[9] = 0.

Programs

  • PARI
    A256299(n,b=9)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~

A256303 Apply the transformation 0 -> 1 -> 2 -> 0 to the digits of n written in base 3; do not convert back to base 10.

Original entry on oeis.org

1, 2, 0, 21, 22, 20, 1, 2, 0, 211, 212, 210, 221, 222, 220, 201, 202, 200, 11, 12, 10, 21, 22, 20, 1, 2, 0, 2111, 2112, 2110, 2121, 2122, 2120, 2101, 2102, 2100, 2211, 2212, 2210, 2221, 2222, 2220, 2201, 2202, 2200, 2011, 2012, 2010, 2021, 2022, 2020, 2001
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 3 variant of A256078 (base 2) and A048379 (base 10). See A256304 - A256308 for bases 4 through 8, A256289 for base 9, and A256293 for the variant where the result is converted back to base 10.

Examples

			a(3) = 21 because 3 = "10" (in base 3) becomes "21".
a(8) = 0 because 8 = "22" (in base 3) becomes "00".

Programs

  • Mathematica
    Table[FromDigits[IntegerDigits[n,3]/.{0->1,1->2,2->0}],{n,0,60}] (* Harvey P. Dale, Jun 17 2022 *)
  • PARI
    A256303(n,b=3)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

A256308 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 0 to the digits of n written in base 8; do not convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 0, 21, 22, 23, 24, 25, 26, 27, 20, 31, 32, 33, 34, 35, 36, 37, 30, 41, 42, 43, 44, 45, 46, 47, 40, 51, 52, 53, 54, 55, 56, 57, 50, 61, 62, 63, 64, 65, 66, 67, 60, 71, 72, 73, 74, 75, 76, 77, 70, 1, 2, 3, 4
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 8 variant of A256078 (base 2) and A048379 (base 10). See A256303 - A256307 for bases 3 through 7, A256289 for base 9, and A256298 for the variant where the result is converted back to base 10.

Examples

			a(8) = 21 because 8 = "10" in base 8 becomes "21".
a(63) = 0 because 63 = "77" in base 8 becomes "00".

Programs

  • Mathematica
    Table[FromDigits[IntegerDigits[n,8]/.{0->1,1->2,2->3,3->4,4->5,5->6,6->7,7->0}],{n,0,60}] (* Harvey P. Dale, Mar 29 2015 *)
  • PARI
    A256308(n,b=8)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

Extensions

Examples corrected by Harvey P. Dale, Mar 29 2015

A169931 a(n) = 2*n in the arithmetic defined in A169918.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 32, 33, 34, 35, 36, 37, 38, 39, 30, 31, 42, 43, 44, 45, 46, 47, 48, 49, 40, 41, 52, 53, 54, 55, 56, 57, 58, 59, 50, 51, 62, 63, 64, 65, 66, 67, 68, 69, 60, 61, 72, 73, 74, 75, 76, 77, 78, 79, 70, 71, 82, 83, 84, 85, 86, 87, 88, 89, 80, 81, 92, 93, 94, 95, 96
Offset: 0

Views

Author

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 20 2010

Keywords

Comments

Equivalently, increase each (decimal) digit by 2 and take each result modulo 10. I.e., apply d -> (d+2 mod 10) to each digit of n. - M. F. Hasler, Mar 25 2015

Crossrefs

Cf. A048379, A169918.

Programs

  • Mathematica
    Table[FromDigits[Mod[IntegerDigits[n]+2,10]],{n,0,100}] (* Harvey P. Dale, Aug 17 2021 *)
  • PARI
    A169931(n)=2*!n+apply(d->(d+2)%10,n=digits(n))*vector(#n,i,10^(#n-i)) \\ M. F. Hasler, Mar 25 2015

Formula

A169931 = A048379 o A048379 (function A048379 applied twice). - M. F. Hasler, Mar 25 2015

A256294 Apply the transformation 0 -> 1 -> 2 -> 3 -> 0 to the digits of n written in base 4, then convert back to base 10.

Original entry on oeis.org

1, 2, 3, 0, 9, 10, 11, 8, 13, 14, 15, 12, 1, 2, 3, 0, 37, 38, 39, 36, 41, 42, 43, 40, 45, 46, 47, 44, 33, 34, 35, 32, 53, 54, 55, 52, 57, 58, 59, 56, 61, 62, 63, 60, 49, 50, 51, 48, 5, 6, 7, 4, 9, 10, 11, 8, 13, 14, 15, 12
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 4 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256299 for bases 3 through 9, and A256304 for the variant where the result is not converted back to base 10.

Examples

			a(4) = 7 because 4 = 10[4] becomes 21[4] = 9.
a(15) = 0 because 15 = 33[4] becomes 00[4] = 0.

Programs

  • PARI
    A256294(n,b=4)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~

A256298 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 0 to the digits of n written in base 8, then convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 0, 17, 18, 19, 20, 21, 22, 23, 16, 25, 26, 27, 28, 29, 30, 31, 24, 33, 34, 35, 36, 37, 38, 39, 32, 41, 42, 43, 44, 45, 46, 47, 40, 49, 50, 51, 52, 53, 54, 55, 48, 57, 58, 59, 60, 61, 62, 63, 56, 1, 2, 3, 4
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 8 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256299 for bases 3 through 9, and A256308 for the variant where the result is not converted back to base 10.

Examples

			a(8) = 17 because 8 = 10[8] becomes 21[8] = 17.
a(63) = 0 because 63 = 77[8] becomes 00[8] = 0.

Links

Programs

  • Mathematica
    Table[FromDigits[IntegerDigits[n,8]+1/.(8->0),8],{n,0,60}] (* Harvey P. Dale, Jan 28 2023 *)
  • PARI
    A256298(n,b=8)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~

A256304 Apply the transformation 0 -> 1 -> 2 -> 3 -> 0 to the digits of n written in base 4; do not convert back to base 10.

Original entry on oeis.org

1, 2, 3, 0, 21, 22, 23, 20, 31, 32, 33, 30, 1, 2, 3, 0, 211, 212, 213, 210, 221, 222, 223, 220, 231, 232, 233, 230, 201, 202, 203, 200, 311, 312, 313, 310, 321, 322, 323, 320, 331, 332, 333, 330, 301, 302, 303, 300, 11, 12, 13, 10, 21, 22, 23, 20, 31, 32
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 4 variant of A256078 (base 2) and A048379 (base 10). See A256303 - A256308 for bases 3 through 8, A256289 for base 9, and A256294 for the variant where the result is converted back to base 10.

Examples

			a(4) = 21 because 4 = "10" (in base 4) becomes "21".
a(15) = 0 because 15 = "33" (in base 4) becomes "00".

Programs

  • PARI
    A256304(n,b=4)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

A256307 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 0 to the digits of n written in base 7; do not convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 0, 21, 22, 23, 24, 25, 26, 20, 31, 32, 33, 34, 35, 36, 30, 41, 42, 43, 44, 45, 46, 40, 51, 52, 53, 54, 55, 56, 50, 61, 62, 63, 64, 65, 66, 60, 1, 2, 3, 4, 5, 6, 0, 211, 212, 213, 214, 215, 216, 210, 221, 222, 223, 224
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 7 variant of A256078 (base 2) and A048379 (base 10). See A256303 - A256308 for bases 3 through 8, A256289 for base 9, and A256297 for the variant where the result is converted back to base 10.

Examples

			a(7) = 21 because 7 = "10" (in base 7) becomes "21".
a(48) = 0 because 48 = "66" (in base 7) becomes "00".

Programs

  • Mathematica
    Table[FromDigits[IntegerDigits[n,7]/.{0->1,1->2,2->3,3->4,4->5,5->6,6->0}],{n,0,60}] (* Harvey P. Dale, Oct 09 2023 *)
  • PARI
    A256307(n,b=7)=!n+eval(Strchr(apply(d->(d+1)%b+48, digits(n,b))))

A256079 Increase each (decimal) digit of n by 1, with carry (i.e., '9' becomes '0' and a (further) increment of 1 of the digit to the left).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76
Offset: 0

Views

Author

M. F. Hasler, Mar 21 2015

Keywords

Comments

Equivalently, add to n the repunit A002275(d) with same number of digits d as n.
See A048379 for the variant without carry, i.e., (cyclic) increase of each digit modulo 10, 0 -> 1 -> ... -> 9 -> 0.

Examples

			a(9) = 9 + 1 = 10, a(10) = 10 + 11 = 21, ..., a(99) = 99 + 11 = 110, a(100) = 100 + 111 = 211, ...

Programs

  • PARI
    a(n)=n+10^#Str(n)\9

Formula

a(n) = n + A002275(A055642(n)).
a(n) = A048379(n) if n has no digit '9'.

A256295 Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 0 to the digits of n written in base 5, then convert back to base 10.

Original entry on oeis.org

1, 2, 3, 4, 0, 11, 12, 13, 14, 10, 16, 17, 18, 19, 15, 21, 22, 23, 24, 20, 1, 2, 3, 4, 0, 56, 57, 58, 59, 55, 61, 62, 63, 64, 60, 66, 67, 68, 69, 65, 71, 72, 73, 74, 70, 51, 52, 53, 54, 50, 81, 82, 83, 84, 80, 86, 87, 88, 89, 85
Offset: 0

Views

Author

M. F. Hasler, Mar 22 2015

Keywords

Comments

Base 5 variant of A035327 (base 2) and A048379 (base 10). See A256293 - A256299 for bases 3 through 9, and A256305 for the variant where the result is not converted back to base 10.

Examples

			a(5) = 11 because 5 = 10[5] becomes 21[5] = 11.
a(24) = 0 because 24 = 44[5] becomes 00[5] = 0.

Programs

  • PARI
    A256295(n,b=5)=!n+apply(t->(t+1)%b,n=digits(n,b))*vector(#n,i,b^(#n-i))~
Previous Showing 11-20 of 25 results. Next

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