

A255589


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


3



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
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OFFSET

0,3


COMMENTS

Fixed points of the transform are listed in A048329.


LINKS

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


FORMULA

a(4*k) = k.
a(4^k) = 4^(k1).


EXAMPLE

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.


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, 4);


MATHEMATICA

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 *)


PROG

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


CROSSREFS

Cf. A030103, A038572, A048329, A255588, A255590A255594, A048787, A255689A255693.
Sequence in context: A080409 A255689 A030103 * A290053 A105640 A090299
Adjacent sequences: A255586 A255587 A255588 * A255590 A255591 A255592


KEYWORD

nonn,easy,base


AUTHOR

Paolo P. Lava, Mar 02 2015


STATUS

approved



