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A255590
Convert n to base 5, move the least significant digit to the most significant one and convert back to base 10.
3
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
0,3
COMMENTS
a(5*n) = n.
a(5^n) = 5^(n-1).
Fixed points of the transform are listed in A048330.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..15625 (terms 0..1000 from Paolo P. Lava)
EXAMPLE
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.
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 *)
PROG
(Python)
def A255590(n):
....x=str(A007091(n))
....return int(x[-1]+x[:-1], 5) # Indranil Ghosh, Feb 03 2017
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, Mar 02 2015
STATUS
approved