A022797 -id:A022797 - cp's OEIS frontend

A125167 Numbers n such that the n-th prime + n-th nonprime is itself prime.

1, 2, 3, 6, 7, 15, 20, 26, 29, 30, 35, 40, 42, 43, 46, 52, 57, 61, 65, 70, 75, 84, 92, 99, 100, 102, 105, 125, 139, 140, 144, 149, 154, 164, 171, 179, 183, 197, 202, 214, 218, 223, 227, 232, 234, 245, 247, 251, 258, 265, 272, 280, 288, 290, 294, 299, 304, 323, 325

Offset: 1

Jason G. Wurtzel, Nov 22 2006

			The 15th prime is 47, while the 15th nonprime is 24. 47+24=71 which is itself prime. Similarly, the 30th prime is 113, while the 30th nonprime is 44. 113+44=157 which is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A018252, A022797.

Module[{nn=500,np,tbl},np=Select[Range[nn],!PrimeQ[#]&];tbl=Table[{n,np[[n]]+Prime[n]},{n,Length[ np]}];Select[tbl,PrimeQ[#[[2]]]&]][[;;,1]] (* Harvey P. Dale, Sep 21 2023 *)

More terms from Klaus Brockhaus, Nov 23 2006

A133795 a(n) = n-th semiprime + n-th non-semiprime.

Original entry on oeis.org

5, 8, 12, 15, 21, 23, 32, 34, 38, 42, 50, 52, 54, 58, 62, 70, 76, 79, 84, 87, 89, 94, 101, 106, 114, 118, 124, 128, 130, 132, 138, 141, 144, 147, 159, 165, 171, 177, 179, 182, 185, 187, 195, 200, 202, 211, 213, 215, 218, 221, 231, 236, 238, 241, 247, 252, 261

Offset: 1

Jonathan Vos Post, Jan 05 2008

Semiprime analog of A022797 n-th prime + n-th nonprime. a(n) is prime for n = 1, 6, 18, 21, 23. a(n) is itself semiprime for n = 4, 5, 22, 25, 38, 39, 57, 62, 69, 77 of which first 10 indices all but n=5 are themselves semiprimes.

			a(1) = 1st semiprime + 1st nonsemiprime = 4 + 1 = 5.
a(2) = 2nd semiprime + 2nd nonsemiprime = 6 + 2 = 8.
a(3) = 3rd semiprime + 3rd nonsemiprime = 9 + 3 = 12.

Cf. A000040, A001358, A022797, A100959.

A100959 := proc(n) option remember; local a ; if n = 1 then 1 ; else for a from A100959(n-1)+1 do if numtheory[bigomega](a) <> 2 then RETURN(a) ; fi ; od: fi ; end: A001358 := proc(n) option remember ; local a ; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A133795 := proc(n) A100959(n)+A001358(n) ; end: seq(A133795(n),n=1..100) ; # R. J. Mathar, Jan 09 2008

Module[{nn=200,spr,non},spr=Select[Range[nn],PrimeOmega[#]==2&];non=Take[ Complement[ Range[ nn],spr],Length[ spr]];Total/@Thread[{spr,non}]] (* Harvey P. Dale, Sep 06 2024 *)

a(n) = A001358(n) + A100959(n).

Corrected and extended by R. J. Mathar, Jan 09 2008

cp's OEIS Frontend

A125167 Numbers n such that the n-th prime + n-th nonprime is itself prime.

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