

A105327


Numbers n such that pi(n)=pi(d_1!)+pi(d_2!)+...+pi(d_k!) where d_1 d_2 ...d_k is the decimal expansion of n.


1



0, 1, 2, 115, 1626, 5370, 5371, 5570, 5571, 6170, 6171, 40854, 373369, 373469, 419386, 419658, 419685, 889609, 889619
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

There is no further term (the proof is easy).


LINKS

Table of n, a(n) for n=1..19.
Eric Weisstein's World of Mathematics, Factorial.


EXAMPLE

889619 is in the sequence because pi(889619)=pi(8!)+pi(8!)+pi(9!)+pi(6!)+pi(1!)+pi(9!).


MATHEMATICA

Do[h = IntegerDigits[m]; l = Length[h]; If[PrimePi[m] == Sum[PrimePi[h[[k]]! ], {k, l}], Print[m]], {m, 0, 3000000}]


CROSSREFS

Cf. A066457, A105328.
Sequence in context: A008271 A209184 A065670 * A260334 A257939 A203607
Adjacent sequences: A105324 A105325 A105326 * A105328 A105329 A105330


KEYWORD

base,fini,full,nonn


AUTHOR

Farideh Firoozbakht, Apr 20 2005


STATUS

approved



