A107120 Numbers m such that pi(m) = prime(d_1*d_2*...*d_k) where d_1 d_2 ... d_k is the decimal expansion of m.

162, 242, 291, 371, 461, 515, 2419, 2815, 11874, 64751, 81927, 264961, 276184, 757155, 2537825, 7717729, 9548491, 14738827, 19728438, 19728446, 19728464, 23695527, 77362954, 269776516, 269776523, 269776532, 358399327, 2385883646, 59955748691, 67893872935, 848472784869

Offset: 1

Author

Farideh Firoozbakht, May 13 2005

Keywords

• nonn
• base
• fini

Comments

A107121 is a subsequence of this sequence (see the comments line of A107121).

a(32) > 7*10^14, if it exists. - Giovanni Resta, Jun 01 2020

The sequence is finite as pi(m) >= pi(10^(k-1)) grows faster than prime(9^k) >= prime(d_1*d_2*...*d_k). - Max Alekseyev, Dec 30 2024

Examples

			23695527 is in the sequence because pi(23695527)=prime(2*3*6*9*5*5*2*7).
		

Crossrefs

Cf. A097223, A107121.

Programs

Mathematica

Do[h = IntegerDigits[m]; l = Length[h]; If[Min[h] > 0 && PrimePi[m] == Prime[Product[h[[k]], {k, l}]], Print[m]], {m, 52000000}]

Extensions

a(23)-a(28) from Donovan Johnson, Jul 12 2010

a(29)-a(31) from Giovanni Resta, Jun 01 2020