A291966 Numerators of fractions with the anomalous cancellation property, corresponding to denominators listed in A291965.

16, 26, 19, 49, 22, 33, 34, 44, 55, 64, 66, 77, 138, 148, 88, 95, 96, 97, 39, 49, 99, 101, 103, 104, 124, 121, 33, 34, 44, 55, 65, 66, 106, 67, 77, 88, 97, 98, 99, 149, 101, 102, 206, 13, 163, 132, 83, 134, 136, 44, 138, 55, 66, 146, 77, 88, 195, 49, 197, 79, 99, 199, 101, 203, 102, 244, 145, 143, 55, 66, 116, 186, 67, 77, 88, 98, 99, 101

Offset

1,1

Comments

See A291965 for more details, comments and references.

Links

Table of n, a(n) for n=1..78.

Example

The two-digit examples 16/64, 26/65, 19/95, 49/98 are well known.
The earliest three-digit terms of A291965 correspond to 34/136 = 4/16, 64/160 = 4/10, 138/184 = 3/4, ...

Prog

(PARI) /* Note: a(n) = A291966(A291965(n))! This function does not yield the n-th term, but the numerator corresponding to denominator N in A291965; if N is not in A291965, it yields zero. */ A291966(n, dn=digits(n), Dn=Set(dn))=local(Cd, sc(x)=select(t->setsearch(Cd, t), x), rd(x)=local(S=0); fromdigits(select(d->!(setsearch(Cd, d)&&!bittest(S, d)&&S+=1<<d), x))); for(d=10, n-1, gcd(d, n)>1 && #(Cd=setintersect(Set(dd=digits(d)), Dn)) && gcd(n, d)%10 ||next; rd(dd) || next; my(n1=rd(dn), d1=rd(dd), nd=digits(n1)); Cd=setintersect(Set(dd=digits(d1)), Set(nd)); if(#Cd, d*rd(nd)==n*rd(dd) && rd(dd), d*n1 == n*d1) && return(d))}
/* To print this sequence: */ for(N=10, 500, A291966(N)&&print1(A291966(N)", "))

Crossrefs

Cf. A291965, A291093/A291094, A159975/A159976, A290462/A290463.

Sequence in context: A267764 A264588 A291093 * A171144 A347692 A204543

Adjacent sequences: A291963 A291964 A291965 * A291967 A291968 A291969

Keyword

nonn,base,frac

Author

M. F. Hasler, Sep 06 2017

Status

approved