A255692 -id:A255692 - cp's OEIS frontend

A255693 Convert n to base 8, move the most significant digit to the least significant one and convert back to base 10.

0, 1, 2, 3, 4, 5, 6, 7, 1, 9, 17, 25, 33, 41, 49, 57, 2, 10, 18, 26, 34, 42, 50, 58, 3, 11, 19, 27, 35, 43, 51, 59, 4, 12, 20, 28, 36, 44, 52, 60, 5, 13, 21, 29, 37, 45, 53, 61, 6, 14, 22, 30, 38, 46, 54, 62, 7, 15, 23, 31, 39, 47, 55, 63, 1, 9, 17, 25, 33, 41

Offset: 0

Paolo P. Lava, Mar 02 2015

a(8*n) = 1.

Fixed points of the transform are listed in A048333.

			13 in base 8 is 15: moving the most significant digit as the least significant one we have 51 that is 41 in base 10.

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Cf. A006257, A030107, A255588-A255594, A255689-A255692.

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 1 to nops(a)-1 do b:=[op(b),a[k]]; od; a:=[a[nops(a)],op(b)];
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(10^4,8);

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 8; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)

A345110 a(n) is n rotated one place to the left or, equivalently, n with the most significant digit moved to the least significant place, omitting leading zeros.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 6, 16, 26, 36, 46, 56, 66, 76, 86

Offset: 0

Felix Fröhlich, Jun 09 2021

First differs from A004086 at n = 101, since A004086(101) = 101, but a(101) = 11.

			For n = 123: When 123 is rotated one place to the left the resulting number is 231, so a(123) = 231.

Cf. A004086, A345111, A345112, A345113, A345114, A345115.

Rotate left in other bases: A006257, A048787, A255689, A255691, A255692, A255693.

Array[FromDigits@*RotateLeft@*IntegerDigits,100,0] (* Giorgos Kalogeropoulos, Jun 09 2021 *)

eva(n) = subst(Pol(n), x, 10)
rot(vec) = if(#vec < 2, return(vec)); my(s=concat(Str(2), ".."), v=[]); s=concat(s, Str(#vec)); v=vecextract(vec, s); v=concat(v, vec[1]); v
a(n) = eva(rot(digits(n)))

def rotl(s): return s[1:] + s[0]
def a(n): return int(rotl(str(n)))
print([a(n) for n in range(69)]) # Michael S. Branicky, Jun 09 2021

A255691 Convert n to base 6, move the most significant digit to the least significant one and convert back to base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 1, 7, 13, 19, 25, 31, 2, 8, 14, 20, 26, 32, 3, 9, 15, 21, 27, 33, 4, 10, 16, 22, 28, 34, 5, 11, 17, 23, 29, 35, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175

Offset: 0

Paolo P. Lava, Mar 02 2015

a(6*n) = 1.

Fixed points of the transform are listed in A048331.

			16 in base 6 is 24: moving the most significant digit as the least significant one we have 42 that is 26 in base 10.

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Cf. A006257, A030105, A255588-A255594, A255689-A255690, A255692-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 1 to nops(a)-1 do b:=[op(b),a[k]]; od; a:=[a[nops(a)],op(b)];
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(10^4,6);

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 6; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 65]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n,6]],6],{n,0,70}] (* Harvey P. Dale, Mar 02 2023 *)

cp's OEIS Frontend

A255693 Convert n to base 8, move the most significant digit to the least significant one and convert back to base 10.

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A345110 a(n) is n rotated one place to the left or, equivalently, n with the most significant digit moved to the least significant place, omitting leading zeros.

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A255691 Convert n to base 6, move the most significant digit to the least significant one and convert back to base 10.

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Maple

Mathematica