A171397 Earliest sequence containing no 11-term arithmetic progression.

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

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);

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

Crossrefs

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

Cf. Numbers 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).

Cf. 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

Status

approved