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A255594
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Convert n to base 9, move least significant digit to most significant digit and convert back to base 10.
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13
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0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 10, 19, 28, 37, 46, 55, 64, 73, 2, 11, 20, 29, 38, 47, 56, 65, 74, 3, 12, 21, 30, 39, 48, 57, 66, 75, 4, 13, 22, 31, 40, 49, 58, 67, 76, 5, 14, 23, 32, 41, 50, 59, 68, 77, 6, 15, 24, 33, 42, 51, 60, 69, 78, 7, 16, 25, 34, 43, 52, 61
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OFFSET
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0,3
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COMMENTS
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Fixed points of the transform are listed in A048334.
For more than 2 base-9 digits, reversal and cyclic shifts of a number start to differ, so this sequence differs from A030108. - Alonso del Arte, Mar 22 2015
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LINKS
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FORMULA
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a(9*n) = n.
a(9^n) = 9^(n-1).
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EXAMPLE
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13 in base 9 is 14: moving the least significant digit as the most significant one we have 41 that is 37 in base 10.
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MAPLE
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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, 9);
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MATHEMATICA
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roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 9; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n, 9]], 9], {n, 0, 80}] (* Harvey P. Dale, Jun 14 2024 *)
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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