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

74, 834, 80940, 809400, 833334, 7414114, 7422694, 7539694, 8094000, 80940000, 809400000, 8094000000, 80940000000, 83335786566, 809400000000, 7539682539694, 8094000000000, 80940000000000

Offset

1,1

Comments

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.

Contains subsequence 834, 833334, 833333333333334, ... formed by numbers (10^k/4 + 2)/3 for k in A296059. - Max Alekseyev, Mar 09 2024

Links

Table of n, a(n) for n=1..18.

Example

phi(74) = 36 that is the 10's complement of the digits of 74.

Maple

with(numtheory): P:=proc(q) local a, b, k, n;
for n from 1 to q do a:=convert(phi(n), base, 10);
for k from 1 to nops(a) do a[k]:=(10-a[k]) mod 10; od; b:=0;
for k from 1 to nops(a) do b:=b*10+a[nops(a)-k+1]; od;
if b=n then print(n); fi; od; end: P(10^9);

Prog

(PARI) isok(x) = {my(dx = digits(x), dy = vector(#dx, k, (10-dx[k]) % 10)); fromdigits(dy) == eulerphi(x); } \\ Michel Marcus, Mar 12 2018

Crossrefs

Cf. A000010, A055120, A296059.

Sequence in context: A250913 A186124 A204353 * A222861 A242146 A007033

Adjacent sequences: A300484 A300485 A300486 * A300488 A300489 A300490

Keyword

nonn,base,more

Author

Paolo P. Lava, Mar 07 2018

Extensions

a(11)-a(15) from Giovanni Resta, Mar 09 2018

a(16)-a(18) from Max Alekseyev, Mar 09 2024

Status

approved