OFFSET
1,1
COMMENTS
The only numbers with the property that pi(n) = sum of the digits of n, are the three numbers 15, 27 & 39.
When n exceeds approximately 10^44, then pi(n) is consistently greater than the product of digits of n. So no term of this sequence exceeds 10^44. In particular, this sequence is finite. - Jeppe Stig Nielsen, Nov 04 2018
Products of digits of terms are in A002473. Term by term up to some bound (such that the bounds on primes hold), one could check terms t in A002473 on some known bounds. See example below. - David A. Corneth, Nov 06 2018
There are no other terms below 10^17. - Max Alekseyev, Nov 07 2024
EXAMPLE
2475998 is in the sequence because pi(2475998)=2*4*7*5*9*9*8.
1152 is in A002473. As 8643 <= prime(1152) <= 9794. Examples of the 13 numbers with product of digits is 1152 in that interval are: 8944, 9288, 9448, 9484 none of which are terms. - David A. Corneth, Nov 06 2018
MATHEMATICA
v={}; Do[If[h=IntegerDigits[n]; l=Length[h]; p=Product[h[[k]], {k, l}]; PrimePi[n]==p, v=Append[v, n]; Print[v], If[Mod[n, 1000000]==0, Print[ -n]]], {n, 200000000}]
Select[Range[2500000], PrimePi[#]==Times@@IntegerDigits[#]&] (* Harvey P. Dale, Dec 04 2012 *)
PROG
(PARI) isok(n) = primepi(n) == factorback(digits(n)); \\ Michel Marcus, Apr 23 2018
(Magma) [n: n in [1..10^5] | &*Intseq((n)) eq #PrimesUpTo(n)]; // Vincenzo Librandi, Nov 06 2018
CROSSREFS
KEYWORD
base,more,nonn,fini
AUTHOR
Farideh Firoozbakht, Aug 02 2004
EXTENSIONS
Keyword fini from Jeppe Stig Nielsen, Nov 04 2018
STATUS
approved