A227857 Number of numbers whose American English name has no letter in common with that of n.

5, 7, 29, 15, 36, 3, 95, 11, 1, 5, 2, 19, 2, 0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 3, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 1, 4, 1, 4, 0, 1, 0, 0, 0, 12, 0, 5, 0, 2, 0, 6, 0, 0, 0, 12, 0, 1, 0, 1, 0, 12, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1

Offset

0,1

Comments

The sequence is well defined and zero for n sufficiently large (> 6.1*10^30 ?) because "million", "billion" etc. have a letter in common with all small numbers except for three, which is letter-disjoint with six. Therefore, 3 is letter-disjoint with six, six million, six billion, six nonillion (10^30) and any nonempty sum of two or more of these. See also example of a(5).

Links

Table of n, a(n) for n=0..99.

E. Angelini, Chaîne de noms de nombres

E. Angelini, Chaîne de noms de nombres [Cached copy, with permission]

OEIS Index entries for sequences related to the English name of numbers

Example

a(0) = 5 = # {6, 50, 56, 60, 66} because "zero" has no letter in common with: six, fifty, fifty-six, sixty, sixty-six.
a(5) = 3 = # {2, 2000, 2002} because "five" has no letter in common with: two, two thousand, two thousand two. ("thousand" is not considered; "one thousand" is excluded.)
a(3) = 15 = 2^4-1 because any nonzero sum_{i=0,6,9,30} e_i*10^i with e_i in {0, 6} is "letter-disjoint" with three.

Prog

(PARI) A227857(n, lang=English/*see A052360*/, L=999, o=0)={n==5 && L+=2000; n==3 && return(15)/*can't be computed explicitely*/; n=setminus(Set(Vec(lang(n))), Set([" ", "-"])); sum(k=o, L, !setintersect( Set(Vec(lang(k))), n))}

Crossrefs

Sequence in context: A179305 A307100 A229337 * A266078 A147993 A213901

Adjacent sequences: A227854 A227855 A227856 * A227858 A227859 A227860

Keyword

nonn,word

Author

M. F. Hasler, Nov 04 2013

Status

approved