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A216194
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a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists).
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14
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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Modified the definition to make the offset 1 by Nathan Fox, Mar 10 2016
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STATUS
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approved
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