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

Author

M. F. Hasler, Nov 04 2013

Keywords

• nonn
• word

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).

Examples

			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.
		

Links

• 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

Programs

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))}