A048331 -id:A048331 - cp's OEIS frontend

A255691 Convert n to base 6, move the most significant digit to the least significant one and convert back to base 10.

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, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175

Offset: 0

Paolo P. Lava, Mar 02 2015

a(6*n) = 1.

Fixed points of the transform are listed in A048331.

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

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Cf. A006257, A030105, A255588-A255594, A255689-A255690, A255692-A255693.

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(10^4,6);

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 6; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 65]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n,6]],6],{n,0,70}] (* Harvey P. Dale, Mar 02 2023 *)

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

Erich Friedman, Feb 19 2001

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

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

Rémy Sigrist, Table of n, a(n) for n = 0..10000

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

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

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)

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

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

Paolo P. Lava, Mar 02 2015

a(6*n) = n.

Fixed points of the transform are listed in A048331.

			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.

Indranil Ghosh, Table of n, a(n) for n = 0..46656 (terms 0..1000 from Paolo P. Lava)

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

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);

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 *)

def A255591(n):
    x=A007092(n)
    return int(x[-1]+x[:-1],6) # Indranil Ghosh, Feb 03 2017

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A255691 Convert n to base 6, move the most significant digit to the least significant one and convert back to base 10.

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A059711 Smallest base in which n is a repdigit.

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python