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 1-10 of 10 results.

A255689 Convert n to base 4, move the most significant digit to the least significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 1, 5, 9, 13, 17, 21, 25
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(4*n) = 1.
Fixed points of the transform are listed in A048329.

Examples

			11 in base 4 is 23: moving the most significant digit as the least significant one we have 32 that is 14 in base 10.

Links

Crossrefs

Cf. A006257, A030103, A255588-A255594, A048787, A255690-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 1 to nops(a)-1 do b:=[op(b),a[k]]; od; a:=[a[nops(a)],op(b)];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,4);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 4; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 70]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n,4]],4],{n,0,70}] (* Harvey P. Dale, Aug 07 2015 *)
  • Python
    def A255689(n):
    x=A007090(n)
    return int (x[1:]+x[0],4) # Indranil Ghosh, Feb 08 2017

A255588 Convert n to base 3, move the least significant digit to the most significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 1, 4, 7, 2, 5, 8, 3, 12, 21, 4, 13, 22, 5, 14, 23, 6, 15, 24, 7, 16, 25, 8, 17, 26, 9, 36, 63, 10, 37, 64, 11, 38, 65, 12, 39, 66, 13, 40, 67, 14, 41, 68, 15, 42, 69, 16, 43, 70, 17, 44, 71, 18, 45, 72, 19, 46, 73, 20, 47, 74, 21, 48, 75, 22, 49, 76, 23
Offset: 0

Views

Author

Paolo P. Lava, Feb 27 2015

Keywords

Comments

a(3*n) = n.
Fixed points of the transform are listed in A048328.

Examples

			10 in base 3 is 101: moving the least significant digit to the most significant one we have 110 that is 12 in base 10.

Links

Crossrefs

Cf. A030102, A038572, A048328, A255589-A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,3);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 3; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,3]],3],{n,0,70}] (* Harvey P. Dale, Feb 20 2022 *)
  • Python
    def A255588(n):
    x=A007089(n)
    return int(x[-1]+x[:-1], 3) # Indranil Ghosh, Feb 03 2017

A255594 Convert n to base 9, move least significant digit to most significant digit and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 10, 19, 28, 37, 46, 55, 64, 73, 2, 11, 20, 29, 38, 47, 56, 65, 74, 3, 12, 21, 30, 39, 48, 57, 66, 75, 4, 13, 22, 31, 40, 49, 58, 67, 76, 5, 14, 23, 32, 41, 50, 59, 68, 77, 6, 15, 24, 33, 42, 51, 60, 69, 78, 7, 16, 25, 34, 43, 52, 61
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

Fixed points of the transform are listed in A048334.
For more than 2 base-9 digits, reversal and cyclic shifts of a number start to differ, so this sequence differs from A030108. - Alonso del Arte, Mar 22 2015

Examples

			13 in base 9 is 14: moving the least significant digit as the most significant one we have 41 that is 37 in base 10.

Links

Crossrefs

Cf. A030108, A038572, A048334, A255588-A255593, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,9);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 9; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,9]],9],{n,0,80}] (* Harvey P. Dale, Jun 14 2024 *)

Formula

a(9*n) = n.
a(9^n) = 9^(n-1).

A345110 a(n) is n rotated one place to the left or, equivalently, n with the most significant digit moved to the least significant place, omitting leading zeros.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 6, 16, 26, 36, 46, 56, 66, 76, 86
Offset: 0

Views

Author

Felix Fröhlich, Jun 09 2021

Keywords

Comments

First differs from A004086 at n = 101, since A004086(101) = 101, but a(101) = 11.

Examples

			For n = 123: When 123 is rotated one place to the left the resulting number is 231, so a(123) = 231.

Crossrefs

Cf. A004086, A345111, A345112, A345113, A345114, A345115.
Rotate left in other bases: A006257, A048787, A255689, A255691, A255692, A255693.

Programs

  • Mathematica
    Array[FromDigits@*RotateLeft@*IntegerDigits,100,0] (* Giorgos Kalogeropoulos, Jun 09 2021 *)
  • PARI
    eva(n) = subst(Pol(n), x, 10)
rot(vec) = if(#vec < 2, return(vec)); my(s=concat(Str(2), ".."), v=[]); s=concat(s, Str(#vec)); v=vecextract(vec, s); v=concat(v, vec[1]); v
a(n) = eva(rot(digits(n)))
  • Python
    def rotl(s): return s[1:] + s[0]
def a(n): return int(rotl(str(n)))
print([a(n) for n in range(69)]) # Michael S. Branicky, Jun 09 2021

A255589 Convert n to base 4, move the least significant digit to the most significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 20, 36, 52, 5, 21, 37, 53, 6, 22, 38, 54, 7, 23, 39, 55, 8, 24, 40, 56, 9, 25, 41, 57, 10, 26, 42, 58, 11, 27, 43, 59, 12, 28, 44, 60, 13, 29, 45, 61, 14, 30, 46, 62, 15, 31, 47, 63, 16, 80, 144, 208, 17, 81
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

Fixed points of the transform are listed in A048329.

Examples

			11 in base 4 is 23: moving the least significant digit to the most significant one we have 32 that is 14 in base 10.

Links

Crossrefs

Cf. A030103, A038572, A048329, A255588, A255590-A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,4);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 4; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Array[FromDigits[RotateRight[IntegerDigits[#,4]],4]&,70,0] (* Harvey P. Dale, Mar 01 2016 *)
  • Python
    def A255589(n):
    x=str(A007090(n))
    return int(x[-1]+x[:-1],4) # Indranil Ghosh, Feb 03 2017

Formula

a(4*k) = k.
a(4^k) = 4^(k-1).

A255590 Convert n to base 5, move the least significant digit to the most significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 1, 6, 11, 16, 21, 2, 7, 12, 17, 22, 3, 8, 13, 18, 23, 4, 9, 14, 19, 24, 5, 30, 55, 80, 105, 6, 31, 56, 81, 106, 7, 32, 57, 82, 107, 8, 33, 58, 83, 108, 9, 34, 59, 84, 109, 10, 35, 60, 85, 110, 11, 36, 61, 86, 111, 12, 37, 62, 87, 112, 13, 38, 63, 88
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(5*n) = n.
a(5^n) = 5^(n-1).
Fixed points of the transform are listed in A048330.

Examples

			14 in base 5 is 24: moving the least significant digit to the most significant one we have 42 that is 22 in base 10.

Links

Crossrefs

Cf. A030104, A038572, A048330, A255588, A255589, A255591-A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,5);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 5; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 68]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,5]],5],{n,0,100}] (* Harvey P. Dale, Jun 11 2025 *)
  • Python
    def A255590(n):
    x=str(A007091(n))
    return int(x[-1]+x[:-1], 5) # Indranil Ghosh, Feb 03 2017

A255591 Convert n to base 6, move least significant digit to most significant digit and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 1, 7, 13, 19, 25, 31, 2, 8, 14, 20, 26, 32, 3, 9, 15, 21, 27, 33, 4, 10, 16, 22, 28, 34, 5, 11, 17, 23, 29, 35, 6, 42, 78, 114, 150, 186, 7, 43, 79, 115, 151, 187, 8, 44, 80, 116, 152, 188, 9, 45, 81, 117, 153, 189, 10, 46, 82, 118, 154, 190, 11
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(6*n) = n.
Fixed points of the transform are listed in A048331.

Examples

			16 in base 6 is 24: moving the least significant digit to the most significant one we have 42 that is 26 in base 10.

Links

Crossrefs

Cf. A030105, A038572, A048331, A255588-A255590, A255592-A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,6);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 6; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* Michael De Vlieger, Mar 04 2015 *)
  • Python
    def A255591(n):
    x=A007092(n)
    return int(x[-1]+x[:-1],6) # Indranil Ghosh, Feb 03 2017

A255592 Convert n to base 7, move least significant digit to most significant digit and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 1, 8, 15, 22, 29, 36, 43, 2, 9, 16, 23, 30, 37, 44, 3, 10, 17, 24, 31, 38, 45, 4, 11, 18, 25, 32, 39, 46, 5, 12, 19, 26, 33, 40, 47, 6, 13, 20, 27, 34, 41, 48, 7, 56, 105, 154, 203, 252, 301, 8, 57, 106, 155, 204, 253, 302, 9, 58, 107, 156
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(7*n) = n.
a(7^n) = 7^(n-1).
Fixed points of the transform are listed in A048332.

Examples

			11 in base 7 is 14: moving the least significant digit to the most significant one we have 41 that is 29 in base 10.

Links

Crossrefs

Cf. A030106, A038572, A048332, A255588-A255591, A255593, A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,7);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 7; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,7]],7],{n,0,100}] (* Harvey P. Dale, Jan 27 2023 *)

A255593 Convert n to base 8, move least significant digit to most significant digit and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 1, 9, 17, 25, 33, 41, 49, 57, 2, 10, 18, 26, 34, 42, 50, 58, 3, 11, 19, 27, 35, 43, 51, 59, 4, 12, 20, 28, 36, 44, 52, 60, 5, 13, 21, 29, 37, 45, 53, 61, 6, 14, 22, 30, 38, 46, 54, 62, 7, 15, 23, 31, 39, 47, 55, 63, 8, 72, 136, 200, 264, 328
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(8*n) = n.
a(8^n) = 8^(n-1).
Fixed points of the transform are listed in A048333.

Examples

			13 in base 8 is 15: moving the least significant digit as the most significant one we have 51 that is 41 in base 10.

Links

Crossrefs

Cf. A030107, A038572, A048333, A255588-A255592, A255594, A048787, A255689-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,8);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 8; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,8]],8],{n,0,70}] (* Harvey P. Dale, Apr 28 2017 *)

A255690 Convert n to base 5, move the most significant digit to the least significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 1, 6, 11, 16, 21, 2, 7, 12, 17, 22, 3, 8, 13, 18, 23, 4, 9, 14, 19, 24, 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92
Offset: 0

Views

Author

Paolo P. Lava, Mar 02 2015

Keywords

Comments

a(5*n) = 1.
Fixed points of the transform are listed in A048330.

Examples

			14 in base 5 is 24: moving the least significant digit as the most significant one we have 42 that is 22 in base 10.

Links

Crossrefs

Cf. A006257, A030104, A255588-A255594, A048787, A255689, A255691-A255693.

Programs

  • Maple
    with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
a:=convert(n,base,h); b:=[]; for k from 1 to nops(a)-1 do b:=[op(b),a[k]]; od; a:=[a[nops(a)],op(b)];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,5);
  • Mathematica
    roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 5; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 68]) (* Michael De Vlieger, Mar 04 2015 *)
Showing 1-10 of 10 results.

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