A117273 Numbers m such that the product of the digits of m is equal to the number of primes less than m.

16, 53, 63, 364, 437, 545, 573, 829, 963, 5449, 6475, 23797, 67458, 2475998

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006

Keywords

• nonn
• base
• fini
• more

Comments

This sequence is finite with its largest term < 10^70. - Stefan Steinerberger, Apr 24 2006

a(15) > 1.288 * 10^10 if it exists. - Kevin P. Thompson, Oct 19 2021

Examples

			364 is in the sequence because the product of its digits is 3*6*4 = 72 and there are 72 prime numbers smaller than 364.
		

Crossrefs

Cf. A000720, A007954, A097220.

Programs

Mathematica

Select[Range[50000], DigitCount[ # ][[10]] == 0 && Product[i^DigitCount[ # ][[i]], {i, 1, 9}] == PrimePi[ # - 1] &] (* Stefan Steinerberger, Apr 24 2006 *)
g[n_] := Product[IntegerDigits[n][[m]], {m, 1, Length[IntegerDigits[n]]}]; Do[If[g[n] == PrimePi[n], Print[n]], {n, 1, 10000000}] (* Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006 *)

PARI

isok(m) = vecprod(digits(m)) == primepi(m); \\ Michel Marcus, Oct 23 2021

Extensions

More terms from Zak Seidov, Stefan Steinerberger and Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006