cp's OEIS Frontend

A300487 Numbers k whose 10's complement mod 10 of their digits is equal to phi(k), the Euler totient function of k.

%I A300487 #19 Mar 09 2024 18:42:33
%S A300487 74,834,80940,809400,833334,7414114,7422694,7539694,8094000,80940000,
%T A300487 809400000,8094000000,80940000000,83335786566,809400000000,
%U A300487 7539682539694,8094000000000,80940000000000
%N A300487 Numbers k whose 10's complement mod 10 of their digits is equal to phi(k), the Euler totient function of k.
%C A300487 Any number of the form 8094*10^j, with j>0, is part of the sequence because its Euler totient function is 2016*10^j.
%C A300487 Contains subsequence 834, 833334, 833333333333334, ... formed by numbers (10^k/4 + 2)/3 for k in A296059. - _Max Alekseyev_, Mar 09 2024
%e A300487 phi(74) = 36 that is the 10's complement of the digits of 74.
%p A300487 with(numtheory): P:=proc(q) local a,b,k,n;
%p A300487 for n from 1 to q do a:=convert(phi(n),base,10);
%p A300487 for k from 1 to nops(a) do a[k]:=(10-a[k]) mod 10; od; b:=0;
%p A300487 for k from 1 to nops(a) do b:=b*10+a[nops(a)-k+1]; od;
%p A300487 if b=n then print(n); fi; od; end: P(10^9);
%o A300487 (PARI) isok(x) = {my(dx = digits(x), dy = vector(#dx, k, (10-dx[k]) % 10)); fromdigits(dy) == eulerphi(x); } \\ _Michel Marcus_, Mar 12 2018
%Y A300487 Cf. A000010, A055120, A296059.
%K A300487 nonn,base,more
%O A300487 1,1
%A A300487 _Paolo P. Lava_, Mar 07 2018
%E A300487 a(11)-a(15) from _Giovanni Resta_, Mar 09 2018
%E A300487 a(16)-a(18) from _Max Alekseyev_, Mar 09 2024