A038107 -id:A038107 - cp's OEIS frontend

A161183 Terms which occur at least twice in A161182.

1, 9, 16, 25, 53, 78, 82, 89, 115, 120, 130, 152, 161, 178, 196, 224, 233, 235, 250, 256, 265, 286, 291, 300, 301, 314, 315, 325, 347, 357, 360, 368, 381, 391, 397, 419, 428, 430, 456, 468, 479, 483, 484, 494, 495, 512, 528, 570, 577, 589, 591, 608, 610, 620

Offset: 1

Daniel Tisdale, Jun 05 2009

A161182 is not monotonic, so some terms (like 89) listed here are not direct neighbors in A161182. - R. J. Mathar, Jun 22 2009

Cf. A078435, A161182.

A038107 := proc(n) numtheory[pi]( n^2) ; end: A078435 := proc(n) n^2-A038107(n) ; end: A161182 := proc(n) A078435(n)-A078435(n-1) ; end: L := [] ; for n from 1 to 1200 do L := [op(L), A161182(n)] ; od: read("transforms3") ; L := sort(L) ; L := LISTDUPL(L,0) ; # R. J. Mathar, Jun 22 2009

f[n_] := 2n - 1 - PrimePi[n^2] + PrimePi[(n-1)^2];
Select[Split[Array[f, 1000]//Sort], Length[#] >= 2&][[All, 1]]
(* Jean-François Alcover, Mar 07 2023 *)

Edited by N. J. A. Sloane, Jun 07 2009

Missing numbers added by R. J. Mathar, Jun 22 2009

A182564 Number of primes < Fibonacci(n).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 4, 5, 8, 11, 16, 23, 34, 50, 74, 111, 166, 250, 376, 574, 871, 1329, 2033, 3120, 4794, 7396, 11425, 17688, 27426, 42612, 66317, 103298, 161207, 251757, 393790, 616645, 966507, 1516410, 2381429, 3743010, 5888201, 9269519, 14604028, 23023555, 36322186, 57337078, 90565070, 143130478

Offset: 0

Alex Ratushnyak, May 05 2012

nonn

			Fibonacci(7)=13, there are 5 primes less than 13, so a(7)=5.

Cf. A000040, A000045, A006880, A007053, A028505, A038107, A040014.

Table[If[PrimeQ[Fibonacci[n]],PrimePi[Fibonacci[n]-1],PrimePi[ Fibonacci[ n]]],{n,0,50}] (* Harvey P. Dale, Feb 12 2022 *)

a(n) = primepi(fibonacci(n)-1) \\ Michel Marcus, May 13 2013

A342695 a(n) is the number of primes in an n X n square array that do not appear on its border, with the elements of the square array being the numbers from 1..n^2, listed in increasing order by rows.

Original entry on oeis.org

0, 0, 1, 2, 4, 4, 8, 10, 14, 15, 21, 21, 27, 31, 36, 42, 48, 46, 58, 61, 68, 73, 83, 83, 96, 100, 110, 114, 127, 123, 144, 146, 157, 165, 175, 179, 201, 201, 212, 221, 241, 235, 258, 265, 275, 282, 303, 301, 328, 330, 346, 351, 381, 377, 403, 406, 427, 433, 455, 452, 486, 493

Offset: 1

Wesley Ivan Hurt, May 18 2021

nonn

			                                                      [1   2  3  4  5]
                                      [1   2  3  4]   [6   7  8  9 10]
                            [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
                   [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
           [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
------------------------------------------------------------------------
  n         1        2         3            4                 5
------------------------------------------------------------------------
  a(n)      0        0         1            2                 4
------------------------------------------------------------------------
  primes   {}       {}        {5}        {7,11}         {7,13,17,19}
------------------------------------------------------------------------

Cf. A000720 (pi), A038107, A221490, A344316 (on border), A344349.

Table[PrimePi[n*(n - 1)] - PrimePi[n] - Sum[PrimePi[n*k + 1] - PrimePi[n*k], {k, n - 2}], {n, 100}]

a(n) = pi(n*(n-1)) - pi(n) - Sum_{k=1..n-2} (pi(n*k+1) - pi(n*k)).

cp's OEIS Frontend

A161183 Terms which occur at least twice in A161182.

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A182564 Number of primes < Fibonacci(n).

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A342695 a(n) is the number of primes in an n X n square array that do not appear on its border, with the elements of the square array being the numbers from 1..n^2, listed in increasing order by rows.

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