A129146 -id:A129146 - cp's OEIS frontend

A129145 Alternately odd prime and odd composite numbers.

3, 9, 5, 15, 7, 21, 11, 25, 13, 27, 17, 33, 19, 35, 23, 39, 29, 45, 31, 49, 37, 51, 41, 55, 43, 57, 47, 63, 53, 65, 59, 69, 61, 75, 67, 77, 71, 81, 73, 85, 79, 87, 83, 91, 89, 93, 97, 95, 101, 99, 103, 105, 107, 111, 109, 115, 113, 117, 127, 119, 131, 121, 137, 123, 139, 125

Offset: 1

Zak Seidov, Apr 01 2007

nonn

For small n's a(2n) >a(2n-1) (that is for small n's, n-th odd prime less than n-th odd composite number), while for large n's a(2n) A129146

Cf. A065091, A071904, A129131, A129146.

Module[{nn=100,pr,cm,len},pr=Prime[Range[2,nn+1]];cm=Select[Range[ 9,2nn+1,2],CompositeQ];len=Min[Length[pr],Length[cm]];Riffle[Take[ pr,len],Take[cm,len]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2019 *)

from sympy import prime, primepi
def A129145(n):
    if n&1: return prime((n>>1)+2)
    if n==2: return 9
    r = n>>1
    m, k = r, primepi(r) + r + (r>>1)
    while m != k:
        m, k = k, primepi(k) + r + (k>>1)
    return m # Chai Wah Wu, Aug 01 2024

a(2n-1)=A065091(n), a(2n) =A071904(n).

A163504 a(n) = abs(n-th prime minus n-th odd nonprime).

Original entry on oeis.org

1, 6, 10, 14, 14, 14, 16, 16, 16, 16, 18, 14, 14, 14, 16, 12, 10, 14, 10, 10, 12, 8, 8, 4, 2, 2, 2, 4, 6, 4, 8, 10, 14, 14, 20, 18, 22, 22, 24, 28, 32, 28, 36, 34, 36, 34, 42, 52, 52, 52, 50, 54, 54, 62, 62, 62, 66, 66, 70, 72, 70, 78, 90, 92, 92, 92, 100, 102, 110, 106, 108, 112

Offset: 1

Juri-Stepan Gerasimov, Jul 29 2009

nonn

			a(1)=abs(2-1)=1; a(2)=abs(3-9)=6.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A000040, A014076, A129146.

A014076 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+2 by 2 do if not isprime(a) then return a; end if; end do: end if; end proc: A163504 := proc(n) abs(ithprime(n)-A014076(n)) ; end: seq(A163504(n),n=1..80) ; # R. J. Mathar, Oct 10 2009

A014076 := Select[Range[1, 10000, 2], PrimeOmega[#] != 1 &]; Table[Abs[Prime[n] - A014076[[n]]], {n,1,50}] (* G. C. Greubel, Jul 27 2017 *)
Module[{nn=250,onp},onp=Select[Range[1,nn,2],!PrimeQ[#]&];Abs[#[[1]]-#[[2]]]&/@Thread[{Prime[Range[Length[onp]]],onp}]] (* Harvey P. Dale, Dec 07 2024 *)

a(n) = abs(A000040(n)-A014076(n)).

An 8 inserted by R. J. Mathar, Oct 10 2009

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A129145 Alternately odd prime and odd composite numbers.

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A163504 a(n) = abs(n-th prime minus n-th odd nonprime).

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