A171397 - OEIS

%I #34 Aug 31 2024 22:03:47

%S 0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,

%T 28,29,30,31,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,

%U 53,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72

%N Write n in base 10, but then read it as if it were written in base 11: if n = Sum_{i >= 0} d_i*10^i, with 0 <= d_i <= 9}, then a(n) = Sum_{i >= 0} d_i*11^i.

%C This is the sequence of all decimal integers that are created when base 10 numbers are interpreted as base 11 numbers.

%C Numbers without digit A (=10) in their representation in base 11. Complement of A095778. - _François Marques_, Oct 20 2020

%C Original definition: Earliest sequence containing no 11-term arithmetic progression.

%C In general, if p is prime, the earliest sequence containing no p-term arithmetic progression is created when base (p-1) numbers are interpreted as base p numbers.

%D D. E. Arganbright, Mathematical Modeling with Spreadsheets, ABACUS, Vol. 3, #4(1986), 19-31.

%H François Marques, <a href="/A171397/b171397.txt">Table of n, a(n) for n = 0..10000</a>

%e a(53)=58 because 53_11 in base 11 equals 58. - _François Marques_, Oct 20 2020

%p seq(`if`(numboccur (10, convert (n, base, 11))=0, n, NULL), n=0..122);

%p # second Maple program:

%p a:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(n, base, 10)):

%p seq(a(n), n=0..66);  # _Alois P. Heinz_, Aug 30 2024

%t Table[FromDigits[RealDigits[n, 10], 11], {n, 0, 100}] (* _François Marques_, Oct 20 2020 *)

%o (PARI) a(n) = fromdigits(digits(n), 11); \\ _Michel Marcus_, Oct 09 2020

%o (Python)

%o def A171397(n): return int(str(n),11) # _Chai Wah Wu_, Aug 30 2024

%Y Different from A065039. - _Alois P. Heinz_, Sep 07 2011

%Y CNumbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).

%Y Numbers with no digit b-1 in base b : A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), this sequence (b=11).

%K nonn,base,easy

%O 0,3

%A _Paul Weisenhorn_, Jul 11 2011

%E Edited by _N. J. A. Sloane_, Aug 31 2024