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 1-3 of 3 results.

A059711 Smallest base in which n is a repdigit.

Original entry on oeis.org

2, 2, 3, 2, 3, 4, 5, 2, 3, 8, 4, 10, 5, 3, 6, 2, 7, 16, 5, 18, 9, 4, 10, 22, 5, 24, 3, 8, 6, 28, 9, 2, 7, 10, 16, 6, 8, 36, 18, 12, 3, 40, 4, 6, 10, 8, 22, 46, 7, 48, 9, 16, 12, 52, 8, 10, 13, 7, 28, 58, 9, 60, 5, 2, 15, 12, 10, 66, 16, 22, 9, 70, 11, 8, 36, 14, 18, 10, 12, 78, 3, 26, 40, 82, 11, 4
Offset: 0

Views

Author

Erich Friedman, Feb 19 2001

Keywords

Comments

Numbers n such that a(n) < n - 1 correspond to Brazilian numbers (A125134); conversely, positive numbers n such that a(n) >= n - 1 correspond to A220570. - Rémy Sigrist, Apr 04 2018

Examples

			a(13) = 3 since 13 in base 3 is 111.

Links

Crossrefs

Cf. A010785, A125134, A048328, A048329, A048330, A048331, A048332, A048333, A048334, A048335, A048336, A048337, A048338, A048339, A048340, A220570.

Programs

  • PARI
    a(n) = for (b=2, oo, if (#Set(digits(n, b))<=1, return (b))) \\ Rémy Sigrist, Apr 04 2018

Formula

From Rémy Sigrist, Apr 04 2018: (Start)
a(n) <= n - 1 for any n >= 3.
a(2^n-1) = 2 for any n >= 0.
a(A048328(n)) <= 3 for any n >= 0.
a(A048329(n)) <= 4 for any n >= 0.
a(A048330(n)) <= 5 for any n >= 0.
a(A048331(n)) <= 6 for any n >= 0.
a(A048332(n)) <= 7 for any n >= 0.
a(A048333(n)) <= 8 for any n >= 0.
a(A048334(n)) <= 9 for any n >= 0.
a(A010785(n)) <= 10 for any n >= 0.
a(A048335(n)) <= 11 for any n >= 0.
a(A048336(n)) <= 12 for any n >= 0.
a(A048337(n)) <= 13 for any n >= 0.
a(A048338(n)) <= 14 for any n >= 0.
a(A048339(n)) <= 15 for any n >= 0.
a(A048340(n)) <= 16 for any n >= 0.
(End)

Extensions

Example clarified by Harvey P. Dale, Oct 11 2015
Terms a(0) = 2, a(1) = 2 and a(2) = 3 prepended by Rémy Sigrist, Apr 04 2018

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

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 1-3 of 3 results.

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