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

1,1

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000720, A007954, A097220.

Sequence in context: A087973 A351584 A332591 * A137515 A164324 A334643

Adjacent sequences: A117270 A117271 A117272 * A117274 A117275 A117276

Keyword

nonn,base,fini,more

Author

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

Extensions

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

Status

approved