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A255592
Convert n to base 7, move least significant digit to most significant digit and convert back to base 10.
3
0, 1, 2, 3, 4, 5, 6, 1, 8, 15, 22, 29, 36, 43, 2, 9, 16, 23, 30, 37, 44, 3, 10, 17, 24, 31, 38, 45, 4, 11, 18, 25, 32, 39, 46, 5, 12, 19, 26, 33, 40, 47, 6, 13, 20, 27, 34, 41, 48, 7, 56, 105, 154, 203, 252, 301, 8, 57, 106, 155, 204, 253, 302, 9, 58, 107, 156
OFFSET
0,3
COMMENTS
a(7*n) = n.
a(7^n) = 7^(n-1).
Fixed points of the transform are listed in A048332.
LINKS
EXAMPLE
11 in base 7 is 14: moving the least significant digit to the most significant one we have 41 that is 29 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, 7);
MATHEMATICA
roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 7; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n, 7]], 7], {n, 0, 100}] (* Harvey P. Dale, Jan 27 2023 *)
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, Mar 02 2015
STATUS
approved