A216194 -id:A216194 - cp's OEIS frontend

A270032 a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists).

0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 7, 8, 9, 10, 11, 12, 13, 7, 15, 8, 17, 9, 19, 10, 7, 11, 23, 8, 25, 13, 9, 7, 29, 10, 31, 8, 11, 17, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 9, 9, 9, 7, 10, 10, 10, 10, 10, 10, 7, 8, 11, 11, 11, 11, 11, 7, 12, 8, 12, 12, 12

Offset: 1

Nathan Fox, Mar 08 2016

a(n) > 0 for n >= 13 since 16 is n written in base n-6.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 6 and k a prime number.

Nathan Fox, Table of n, a(n) for n = 1..10000

Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270042.

Table[SelectFirst[Range[7, 1200], DigitCount[n, #, 6] > 0 &], {n, 13, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

a(n) = if ((n<13) && (n!=6), 0, my(b=7); while(!vecsearch(Set(digits(n, b)), 6), b++); b); \\ Michel Marcus, Mar 10 2016

A270026 a(n) is the smallest b for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).

Original entry on oeis.org

0, 2, 3, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Nathan Fox, Mar 08 2016

For n > 1, a(n)=2 whenever n+1 is not a power of 2.
It is conjectured that the only terms that are neither 2 nor 3 in this sequence are a(7) and a(32767), which are 7 and 5 respectively.
a(n) > 0 for n >= 2 since the base-n representation of n is 10.

Nathan Fox, Table of n, a(n) for n = 1..40000
Eric Weisstein's World of Mathematics, Ternary

Cf. A117970, A216194.

Table[SelectFirst[Range[2, 1200], DigitCount[n, #, 0] > 0 &], {n, 2, 120}] (* Michael De Vlieger, Mar 09 2016, Version 10 *)

a(n) = if (n==1, 0, my(b=2); while(vecmin(digits(n, b)), b++); b); \\ Michel Marcus, Mar 09 2016

A269724 Numbers which contain no 2's when written in bases 3 through 10.

Original entry on oeis.org

0, 1, 3, 4, 31, 58130496, 58130499, 58130500, 58130703, 58183951, 77810815551163745898450783, 77810815551163745898451143, 61819635578801174196008456415, 61819635578801174196008574451, 61819635578801174196008574771

Offset: 1

Nathan Fox, Mar 03 2016

There are 134 known terms. If a(135) exists, it must exceed 10^2300.

Nathan Fox, Table of n, a(n) for n = 1..134

Cf. A216192, A216194.

isok(n) = {for (b=3, 10, d = digits(n, b); if (vecsearch(vecsort(d,,8),2), return (0));); 1;} \\ Michel Marcus, Mar 06 2016

cp's OEIS Frontend

A270032 a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists).

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A270026 a(n) is the smallest b for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).

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Mathematica

PARI

A269724 Numbers which contain no 2's when written in bases 3 through 10.

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Author

Keywords

Comments

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Crossrefs

Programs

PARI