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

Author

M. F. Hasler, Sep 06 2017

Keywords

• nonn
• base
• frac

Comments

See A291965 for more details, comments and references.

Examples

			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, ...
		

Crossrefs

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

Programs

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<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)","))