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.

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A120052 Number of 11-almost primes less than or equal to 10^n.

Original entry on oeis.org

0, 0, 0, 0, 7, 138, 1878, 23448, 279286, 3230577, 36585097, 407818620, 4490844534, 48972151631, 529781669333, 5693047157230, 60832290450373, 646862625625663, 6849459596884350, 72259172519243461
Offset: 0

Views

Author

Robert G. Wilson v, Feb 07 2006

Keywords

Examples

			There are 7 eleven-almost primes up to 10000: 2048, 3072, 4608, 5120, 6912, 7168, and 7680.

Crossrefs

Cf. A066265, A014613, A116382.
Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.

Programs

  • Mathematica
    AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]]; (* Eric W. Weisstein, Feb 07 2006 *)
Table[AlmostPrimePi[11, 10^n], {n, 12}]

Extensions

a(14) from Robert G. Wilson v, Jan 07 2007
a(15)-a(19) from Henri Lifchitz, Mar 18 2025

A076493 Number of common (distinct) decimal digits of n and n^2.

Original entry on oeis.org

1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1
Offset: 0

Views

Author

Labos Elemer, Oct 21 2002

Keywords

Comments

a(A029783(n)) = 0, a(A189056(n)) > 0; 0 <= a(n) <= 10, see example for first occurrences. [Reinhard Zumkeller, Apr 16 2011]

Examples

			a(2) = #{} = 0: 2^2 = 4;
a(0) = #{0} = 1: 0^2 = 0;
a(10) = #{0,1} = 2: 10^2 = 100;
a(105) = #{0,1,5} = 3: 105^2 = 11025;
a(1025) = #{0,1,2,5} = 4: 1025^2 = 1050625;
a(10245) = #{0,1,2,4,5} = 5: 10245^2 = 104960025;
a(102384) = #{0,1,2,3,4,8} = 6: 102384^2 = 10482483456;
a(1023456789) = #{0 .. 9} = 10: 1023456789^2 = 1047463798950190521.

Links

Crossrefs

Cf. A006880, A076489-A076491.
Cf. A000290, A043537.

Programs

  • Haskell
    import Data.List (intersect, nub)
import Data.Function (on)
a076493 n = length $ (intersect `on` nub . show) n (n^2)
-- Reinhard Zumkeller, Apr 16 2011
  • Mathematica
    Table[Length[Intersection[IntegerDigits[n], IntegerDigits[n^2]]], {n, 1, 100}]

Extensions

Initial 1 added and offset adjusted by Reinhard Zumkeller, Apr 16 2011

A091165 Number of primes of the form 30k + 1 less than 10^n.

Original entry on oeis.org

0, 2, 18, 152, 1189, 9807, 83003, 719984, 6355189, 56878661, 514751823, 4700968833, 43258135129
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091166 Number of primes of the form 30k + 7 less than 10^n.

Original entry on oeis.org

1, 4, 24, 155, 1200, 9812, 83104, 720270, 6356475, 56881453, 514763437, 4701002681, 43258188715
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Programs

  • Mathematica
    a[n_]:=Length[Select[Range[0,Floor[1/30*(-7+10^n)]],PrimeQ[30*#+7]&]]
a/@Range[1,7] (* Julien Kluge, Sep 20 2016 *)

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091167 Number of primes of the form 30k + 11 less than 10^n.

Original entry on oeis.org

0, 3, 22, 154, 1198, 9810, 83101, 720314, 6356197, 56882858, 514765307, 4700992147, 43258234871
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091168 Number of primes of the form 30k + 13 less than 10^n.

Original entry on oeis.org

0, 3, 20, 154, 1203, 9824, 83077, 720110, 6356062, 56883199, 514753678, 4700984929, 43258197713
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091169 Number of primes of the form 30k + 17 less than 10^n.

Original entry on oeis.org

0, 2, 22, 153, 1211, 9809, 83107, 720225, 6355839, 56882586, 514754900, 4700994319, 43258179075
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091170 Number of primes of the form 30k + 19 less than 10^n.

Original entry on oeis.org

0, 2, 18, 150, 1192, 9788, 83010, 720153, 6354987, 56879810, 514749730, 4700977077, 43258170456
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091171 Number of primes of the form 30k + 23 less than 10^n.

Original entry on oeis.org

0, 3, 21, 155, 1198, 9840, 83152, 720363, 6356436, 56882425, 514755769, 4700994974, 43258230232
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014

A091172 Number of primes of the form 30k + 29 less than 10^n.

Original entry on oeis.org

0, 3, 20, 153, 1198, 9805, 83022, 720033, 6356346, 56881516, 514760166, 4700997055, 43258200645
Offset: 1

Views

Author

Robert G. Wilson v, Jan 12 2004

Keywords

Crossrefs

Cf. A091165 + A091166 + A091167 + A091168 + A091169 + A091170 + A091171 + A091172 +3 (for 2, 3 & 5) = A006880.

Extensions

a(11)-a(13) from Hiroaki Yamanouchi, Oct 14 2014
Previous Showing 61-70 of 233 results. Next

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