A261466 -id:A261466 - cp's OEIS frontend

A261461 a(n) is the smallest nonzero number that is not a substring of n in its binary representation.

1, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 4, 7, 4, 4, 4, 5, 5, 5, 5, 7, 4, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3

Offset: 0

Reinhard Zumkeller, Aug 30 2015

A261018(n) = a(A260273(n)).
Is a(n) = A091460(n) for n>1? - R. J. Mathar, Sep 02 2015. The lowest counterexample occurs at a(121) = 5 < 6 = A091460(121). - Álvar Ibeas, Sep 08 2020
a(A062289(n))=A261922(A062289(n)); a(A126646(n))!=A261922(A126646(n)). - Reinhard Zumkeller, Sep 17 2015

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
David Consiglio, Jr., Python Program

Cf. A007088, A030308, A260273, A261018; record values and where they occur: A261466, A261467.
See A261922 for a variant.
Cf. A062289, A144016, A261922, A126646.

import Data.List (isInfixOf)
a261461 x = f $ tail a030308_tabf where
   f (cs:css) = if isInfixOf cs (a030308_row x)
                   then f css else foldr (\d v -> 2 * v + d) 0 cs

fQ[m_, n_] := Block[{g}, g[x_] := ToString@ FromDigits@ IntegerDigits[x, 2]; StringContainsQ[g@ n, g@ m]]; Table[k = 1; While[fQ[k, n] && k < n, k++]; k, {n, 85}] (* Michael De Vlieger, Sep 21 2015 *)

from itertools import count
def a(n):
    b, k = bin(n)[2:], 1
    return next(k for k in count(1) if bin(k)[2:] not in b)
print([a(n) for n in range(86)]) # Michael S. Branicky, Feb 26 2023

a(n) = A144016(n) + 1 for any n > 0. - Rémy Sigrist, Mar 10 2018

A261467 Where records occur in A261461.

Original entry on oeis.org

0, 1, 2, 6, 12, 44, 92, 184, 1208, 1256, 4792, 9912, 19832, 39664, 563952, 576464, 4496112, 4499184, 17996528, 17997488, 143972080, 145057520, 145070832, 294967024, 589944560, 1179889136, 2359778272, 71079255008, 72019201952

Offset: 1

Reinhard Zumkeller, Aug 30 2015

A261461(a(n)) = A261466(n).

Rémy Sigrist, C program

Cf. A261461, A261466.

C
```
See Links section.
```

a261467 n = a261467_list !! (n-1)
-- where a261467_list is defined in A261466.

from itertools import count, islice
def f(n):
    b, k = bin(n)[2:], 1
    return next(k for k in count(1) if bin(k)[2:] not in b)
def agen(record=-1):
    yield from (((record:=f(k)), k)[1] for k in count(0) if f(k) > record)
print(list(islice(agen(), 18))) # Michael S. Branicky, Feb 26 2023

Leading zero and more terms from Rémy Sigrist, Mar 10 2018

a(26)-a(29) from Rémy Sigrist, Feb 26 2023

A262360 Fixed points of A262356 and of A262358.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 42, 4410, 3060996

Offset: 1

Reinhard Zumkeller, Sep 19 2015

A261466(a(n)) = a(n).

Table of n, a(n) for n = 1..15

Cf. A262356, A262358.

a262360 n = a262360_list !! (n-1)
a262360_list = [x | x <- [1..], a262356 x == x]

a(15) from Alois P. Heinz, Sep 20 2015

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A261461 a(n) is the smallest nonzero number that is not a substring of n in its binary representation.

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A261467 Where records occur in A261461.

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A262360 Fixed points of A262356 and of A262358.

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