A255590 -id:A255590 - cp's OEIS frontend

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

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

Paolo P. Lava, Mar 02 2015

Fixed points of the transform are listed in A048329.

			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.

Indranil Ghosh, Table of n, a(n) for n = 0..16384 (terms 0..1000 from Paolo P. Lava)

Cf. A030103, A038572, A048329, A255588, A255590-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(10^4,4);

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 *)

def A255589(n):
    x=str(A007090(n))
    return int(x[-1]+x[:-1],4) # Indranil Ghosh, Feb 03 2017

a(4*k) = k.

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula