login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216194 a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists). 14
0, 3, 0, 0, 3, 3, 3, 3, 4, 4, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 10, 3, 4, 11, 3, 3, 3, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 4, 3, 6, 5, 3, 3, 3, 3, 4, 4, 3, 6, 4, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n)=3 if and only if n is in A074940.
a(n) > 0 for n >= 5 since 12 is n written in base n-2.
The only perfect k-th powers (k>=2) that can appear in this sequence are 2^k with k a prime number.
The first n for which a(n)=7 is 849.
The first n for which a(n)=8 is 1084.
The first n for which a(n)=10 is 28. The second is 243.
The first n for which a(n)=11 is 31. The second is 58130496.
a(n)<=11 for all n with fewer than 3000 base 10 digits. No n for which a(n)>11 has been found.
LINKS
MAPLE
firstNTerms:=proc(n) local b, i, rep, L:
L:=[]:
for i from 5 to n do
b:=3:
while true do
rep:=convert(i, base, b):
if evalb(2 in rep) then
L:=[op(L), b]:
break:
fi:
b:=b+1:
od:
od:
L:
end:
MATHEMATICA
sb2[n_]:=Module[{b=3}, While[DigitCount[n, b, 2]<1, b++]; b]; Array[sb2, 110, 5] (* Harvey P. Dale, Jan 16 2016 *)
Table[SelectFirst[Range[3, 1200], DigitCount[n, #, 2] > 0 &], {n, 5, 120}] (* Michael De Vlieger, Mar 09 2016, Version 10 *)
PROG
(PARI) a(n) = if ((n<5) && (n!=2), 0, my(b=3); while (! vecsearch(vecsort(digits(n, b)), 2), b++); b); \\ Michel Marcus, Aug 06 2014, Mar 11 2016
CROSSREFS
Sequence in context: A178153 A267794 A282499 * A365462 A279168 A111787
KEYWORD
nonn,easy,base
AUTHOR
Nathan Fox, Mar 12 2013
EXTENSIONS
Modified the definition to make the offset 1 by Nathan Fox, Mar 10 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 09:56 EDT 2024. Contains 371967 sequences. (Running on oeis4.)