cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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.

Original entry on oeis.org

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

Views

Author

Farideh Firoozbakht, May 13 2005

Keywords

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

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

A107122 Numbers m such that m=prime(prime(prime(d_1*d_2*...*d_k))) where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

31, 161159, 2935241, 12393851, 25792148743, 8378273888129
Offset: 1

Views

Author

Farideh Firoozbakht, May 13 2005, May 27 2008

Keywords

Comments

a(7) > 7*10^14, if it exists. - Giovanni Resta, Jun 01 2020
The sequence is finite as m > 10^(k-1) grows faster than prime(prime(prime(9^k))) >= prime(prime(prime(d_1*d_2*...*d_k))). - Max Alekseyev, Dec 30 2024

Examples

			12393851 is in the sequence because 12393851 = prime(prime(prime(1*2*3*9*3*8*5*1))).
		

Crossrefs

Programs

  • Mathematica
    Do[h= IntegerDigits[Prime[m]];l = Length[h];If[Min[h] > 0 && m == Prime[Prime[Prime[Product[h[[k]], {k, l}]]], Print[Prime[m]]]], {m, 10000000}]

Extensions

a(6) from Giovanni Resta, Jun 01 2020
Showing 1-2 of 2 results.