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 1-4 of 4 results.

A101225 Numbers formed by the third nesting of pi(10^n).

Original entry on oeis.org

1, 4, 12, 46, 194, 977, 5492, 33666, 220068, 1513371, 10833076, 80104927, 608455060, 4726881850, 37431015268, 301327263751, 2460711566651, 20348625806080, 170149286304116, 1436870802519360, 12241980697771924, 105136072207222852, 909475787902559408, 7919305232077304848
Offset: 1

Views

Author

Cino Hilliard, Dec 15 2004

Keywords

Examples

			a(3) = pi(pi(pi(10^3))) = 12, the third entry in the table.

Links

Crossrefs

Cf. A006880, A096359.

Programs

  • Mathematica
    f[n_] := Nest[PrimePi, 10^n, 3]; Table[ f[n], {n, 13}] (* Robert G. Wilson v, Dec 20 2004 *)
  • PARI
    nestpi(n,m) = { local(x,y,z); for(x=1,n,z=10^x;for(y=1,m,z=primepi(z));print1(z",")) }

Formula

a(n) = pi(pi(pi(10^n))) where pi(x) is the number of primes <= x.

Extensions

More terms from Robert G. Wilson v, Dec 20 2004
a(16)-a(24) from Robert G. Wilson v, Mar 11 2015

A374151 The number of prime-indexed primes below 2^n.

Original entry on oeis.org

0, 0, 1, 2, 3, 5, 7, 11, 16, 25, 39, 63, 103, 172, 290, 490, 844, 1464, 2564, 4522, 8022, 14325, 25686, 46382, 84115, 153327, 280423, 514798, 948374, 1752639, 3248574, 6037968, 11250482, 21013808, 39336188, 73788697, 138689231, 261150360, 492602752, 930716294
Offset: 0

Views

Author

Amiram Eldar, Jun 29 2024

Keywords

Comments

The data was calculated using Kim Walisch's primecount program.

Examples

			a(1) = 0 since primepi(primepi(2^1)) = primepi(primepi(2)) = primepi(1) = 0.
a(2) = 1 since primepi(primepi(2^2)) = primepi(primepi(4)) = primepi(2) = 1.

Links

Crossrefs

Cf. A000720, A006450, A007053, A096359, A374150.

Programs

  • Mathematica
    Table[PrimePi[PrimePi[2^n]], {n, 0, 40}]
  • PARI
    a(n) = primepi(primepi(2^n));

Formula

a(n) = A000720(A007053(n)).
a(n) = A132090(2^n).

A092252 a(n) = prime(prime(10^n)).

Original entry on oeis.org

3, 109, 3911, 80917, 1366661, 20491057, 285058399, 3767321791, 47991893393, 594421377761, 7201814452873, 85713609222697, 1005238339412819, 11644468481142713, 133472665317708923, 1516047373452105311
Offset: 0

Views

Author

Cino Hilliard, Feb 19 2004

Keywords

Links

Crossrefs

Cf. A000040, A006450, A006988, A096359.

Programs

  • Mathematica
    Table[Prime[Prime[10^n]], {n, 0, 10}] (* Amiram Eldar, Jun 29 2024 *)
  • PARI
    a(n) = prime(prime(10^n)); \\ Amiram Eldar, Jun 29 2024

Formula

a(n) = A006450(10^n) = A000040(A006988(n)). - Amiram Eldar, Jun 29 2024

Extensions

a(9)-a(10) from Dennis Kluk, Nov 27 2005
a(11)-a(15) using Kim Walisch's primecount added by Amiram Eldar, Jun 29 2024

A101226 Numbers formed by the fourth nesting of pi(10^n).

Original entry on oeis.org

0, 2, 5, 14, 44, 165, 725, 3607, 19624, 115127, 716177, 4675144, 31743253, 222710685, 1606581461, 11868655658, 89506275569, 687275710608, 5361744667232, 42423406909091, 339921273158836, 2754682455861719, 22553369622588850, 186375668479844528
Offset: 1

Views

Author

Cino Hilliard, Dec 15 2004

Keywords

Examples

			a(3) = pi(pi(pi(pi(10^3)))) = 5, the third entry in the table.

Links

Crossrefs

Cf. A000720, A006880, A096359, A101225.

Programs

  • Mathematica
    f[n_] := Nest[PrimePi, 10^n, 4]; Table[ f[n], {n, 13}] (* Robert G. Wilson v, Dec 21 2004 *)
  • PARI
    nestpi(n,m) = { my(x,y,z); for(x=1, n, z=10^x; for(y=1, m, z=primepi(z)); print1(z", ")) } \\ try call nestpi(11, 4)

Formula

a(n) = pi(pi(pi(pi(10^n)))) where pi(x) is the number of primes <= x.
a(n) = A000720(A101225(n)). - Amiram Eldar, Jun 29 2024

Extensions

a(10)-a(13) from Robert G. Wilson v, Dec 21 2004
a(14)-a(24) using Kim Walisch's primecount added by Amiram Eldar, Jun 29 2024
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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