A255589 -id:A255589 - cp's OEIS frontend

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

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

Paolo P. Lava, Feb 27 2015

a(3*n) = n.

Fixed points of the transform are listed in A048328.

			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.

Indranil Ghosh, Table of n, a(n) for n = 0..19683 (terms 0..1000 Paolo P. Lava)

Cf. A030102, A038572, A048328, A255589-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(10^4,3);

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 *)

def A255588(n):
    x=A007089(n)
    return int(x[-1]+x[:-1], 3) # Indranil Ghosh, Feb 03 2017

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

Paolo P. Lava, Mar 02 2015

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

			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.

Indranil Ghosh, Table of n, a(n) for n = 0..15625 (terms 0..1000 from Paolo P. Lava)

Cf. A030104, A038572, A048330, A255588, A255589, A255591-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(10^4,5);

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 *)

def A255590(n):
    x=str(A007091(n))
    return int(x[-1]+x[:-1], 5) # Indranil Ghosh, Feb 03 2017

cp's OEIS Frontend

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

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