A097220 Numbers n such that pi(n) = product of digits of n.

16, 17, 63, 73, 364, 437, 545, 573, 963, 6475, 23797, 67458, 2475989, 2475998

Offset

1,1

Comments

Next term is greater than 2*10^8. The only numbers with the property that pi(n) = sum of the digits of n, are the three numbers 15, 27 & 39.

a(15) > 10^13, if it exists. - Giovanni Resta, Sep 02 2017

a(15) > 10^15, if it exists. - Chai Wah Wu, Apr 23 2018

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

Links

Table of n, a(n) for n=1..14.

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

Cf. A002473, A007954, A000720.

Cf. A097221, A097222, A097223.

Sequence in context: A042205 A041522 A097221 * A041530 A041528 A112012

Adjacent sequences: A097217 A097218 A097219 * A097221 A097222 A097223

Keyword

base,more,nonn,fini

Author

Farideh Firoozbakht, Aug 02 2004

Extensions

Keyword fini from Jeppe Stig Nielsen, Nov 04 2018

Status

approved