A095778 Values of n for which A095777(n) is 9 (those terms which are expressible in decimal digits for bases 2 through 10, but not for base 11).

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 352, 353

Offset

1,1

Comments

Numbers with at least one digit A (=10) in their representation in base 11. Complementary sequence to A171397. - François Marques, Oct 11 2020

Links

François Marques, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Example

a(5)=54 because 54 when expressed in successive bases starting at 2 will produce its first non-decimal digit at base 11. Like so: 110110, 2000, 312, 204, 130, 105, 66, 60, 54. In base 11, 54 is 4A.

Maple

S := []; for n from 1 to 1000 do; if 1>0 then; ct := 0; ok := true; b := 2; if (n>9) then; while ok=true do; L := convert(n, base, b); for e in L while ok=true do; if (e > 9) then ok:=false; fi; od; if ok=true then; ct := ct + 1; b := b + 1; fi; od; fi; if ct=9 then S := [op(S), n]; fi; fi; od; S;
# or
seq(`if`(numboccur(10, convert(n, base, 11))>0, n, NULL), n=0..1000); # François Marques, Oct 11 2020

Mathematica

Select[Range[400], Max[IntegerDigits[#, 11]]>9&] (* Harvey P. Dale, Sep 30 2018 *)

Prog

(PARI) isok(m) = #select(x->(x==10), digits(m, 11)) >= 1; \\ François Marques, Oct 11 2020

Crossrefs

Cf. A095777.

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), this sequence (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), A171397 (b=11).

Sequence in context: A098954 A346261 A061470 * A065438 A017509 A184989

Adjacent sequences: A095775 A095776 A095777 * A095779 A095780 A095781

Keyword

base,nonn

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jun 05 2004

Status

approved