A171397 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.

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, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72

Offset

0,3

Comments

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

Numbers without digit A (=10) in their representation in base 11. Complement of A095778. - François Marques, Oct 20 2020

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

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.

References

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

Links

François Marques, Table of n, a(n) for n = 0..10000

Example

a(53)=58 because 53_11 in base 11 equals 58. - François Marques, Oct 20 2020

Maple

seq(`if`(numboccur (10, convert (n, base, 11))=0, n, NULL), n=0..122);
# second Maple program:
a:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(n, base, 10)):
seq(a(n), n=0..66);  # Alois P. Heinz, Aug 30 2024

Mathematica

Table[FromDigits[RealDigits[n, 10], 11], {n, 0, 100}] (* François Marques, Oct 20 2020 *)

Prog

(PARI) a(n) = fromdigits(digits(n), 11); \\ Michel Marcus, Oct 09 2020
(Python)
def A171397(n): return int(str(n), 11) # Chai Wah Wu, Aug 30 2024

Crossrefs

Different from A065039. - Alois P. Heinz, Sep 07 2011

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).

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).

Sequence in context: A063742 A014089 A065039 * A336557 A335235 A023804

Adjacent sequences: A171394 A171395 A171396 * A171398 A171399 A171400

Keyword

nonn,base,easy

Author

Paul Weisenhorn, Jul 11 2011

Extensions

Edited by N. J. A. Sloane, Aug 31 2024

Status

approved