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

%I A291966 #11 Mar 14 2025 04:27:01
%S A291966 16,26,19,49,22,33,34,44,55,64,66,77,138,148,88,95,96,97,39,49,99,101,
%T A291966 103,104,124,121,33,34,44,55,65,66,106,67,77,88,97,98,99,149,101,102,
%U A291966 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
%N A291966 Numerators of fractions with the anomalous cancellation property, corresponding to denominators listed in A291965.
%C A291966 See A291965 for more details, comments and references.
%e A291966 The two-digit examples 16/64, 26/65, 19/95, 49/98 are well known.
%e A291966 The earliest three-digit terms of A291965 correspond to 34/136 = 4/16, 64/160 = 4/10, 138/184 = 3/4, ...
%o A291966 (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))}
%o A291966 /* To print this sequence: */ for(N=10,500,A291966(N)&&print1(A291966(N)","))
%Y A291966 Cf. A291965, A291093/A291094, A159975/A159976, A290462/A290463.
%K A291966 nonn,base,frac
%O A291966 1,1
%A A291966 _M. F. Hasler_, Sep 06 2017