A066066 -id:A066066 - cp's OEIS frontend

A071186 Numbers k such that prime(2k)-2prime(k) is prime.

3, 4, 5, 6, 10, 11, 13, 15, 18, 19, 20, 26, 29, 33, 34, 37, 42, 43, 44, 49, 50, 60, 61, 62, 64, 65, 66, 72, 77, 79, 84, 89, 91, 92, 96, 97, 98, 99, 101, 103, 105, 109, 112, 118, 120, 126, 127, 128, 129, 130, 133, 135, 140, 144, 146, 152, 153, 155, 163, 166, 172, 173

Offset: 1

Benoit Cloitre, Jun 10 2002

Numbers k such that A066066(k) is prime. - Amiram Eldar, May 19 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000040, A031215, A066066, A100484.

Select[Range[200], PrimeQ[Prime[2*#] - 2*Prime[#]] &] (* Amiram Eldar, May 19 2022 *)

for(n=1,251,if(isprime(prime(2*n)-2*prime(n))==1,print1(n,",")))

A074766 a(n) = prime(2n) - 2*prime(n) - n.

Original entry on oeis.org

-2, -1, 0, 1, 2, 5, 2, 7, 6, 3, 6, 3, 6, 7, 4, 9, 4, 11, 10, 11, 14, 13, 10, 21, 10, 11, 18, 21, 24, 25, 8, 17, 10, 25, 16, 21, 22, 19, 24, 23, 22, 29, 18, 27, 24, 35, 22, 9, 18, 33, 40, 39, 42, 37, 32, 31, 24, 41, 34, 37, 46, 35, 24, 33, 42, 43, 28, 27, 24, 41, 44, 37, 32, 37, 30, 39, 32

Offset: 1

Werner D. Sand, Sep 29 2002

sign

Conjecture: p(2n) - 2p(n) < 2n for all n.

			a(9) = p(18) - 2p(9) - 9 = 61 - 2*23 - 9 = 6.

Cf. A066066.

A074766:=n->ithprime(2*n)-2*ithprime(n)-n: seq(A074766(n), n=1..100); # Wesley Ivan Hurt, Jan 16 2017

Table[Prime[2 n] - 2 Prime[n] - n, {n, 80}] (* Harvey P. Dale, Mar 04 2017 *)

a(n) = A066066(n) - n.

A230329 Prime(prime(2n)) - 2prime(n).

Original entry on oeis.org

1, 11, 31, 53, 87, 131, 157, 203, 237, 295, 339, 387, 465, 501, 523, 633, 679, 755, 833, 889, 941, 1013, 1051, 1231, 1253, 1297, 1391, 1455, 1523, 1597, 1659, 1801, 1825, 1991, 2053, 2115, 2235, 2321, 2385, 2457, 2551, 2657, 2727, 2843, 2905

Offset: 1

Gerasimov Sergey, Oct 16 2013

For n = 12239, 24046, 24140, 24255, ... a(n+1) = a(n), and for n = 2154, 2524, 2810, 3795, ... a(n+1) < a(n). What is the smallest number n such that a(n+2) <= a(n+1) <= a(n)? - Farideh Firoozbakht, Oct 18 2013

Using the Prime Number Theorem, prime(n) ~ n log n, the asymptotic behavior is the same as that of A217622, a(n) ~ 2n (log 2n) log(2n log 2n). - M. F. Hasler, Oct 19 2013

Cf. A230098, A230285, A066066.

Table[Prime[Prime[2n]] - 2Prime[n], {n, 45}]

A230329(n)=prime(prime(2*n))-2*prime(n) \\ M. F. Hasler, Oct 19 2013

a(n) = A217622(n) - 2*A000040(n).

a(n) = A217622(n) - A100484(n). - Omar E. Pol, Oct 19 2013

Corrected by R. J. Mathar, Oct 18 2013

A360206 Triangular array T(m,n) read by antidiagonals: T(m,n) = prime(m+n) - prime(m) - prime(n).

Original entry on oeis.org

-1, 0, 1, 0, 3, 3, 2, 3, 5, 5, 0, 3, 3, 5, 7, 2, 3, 5, 9, 7, 11, 0, 3, 7, 7, 9, 11, 9, 2, 7, 7, 11, 11, 11, 11, 15, 4, 5, 9, 11, 9, 11, 13, 17, 15, 0, 5, 7, 7, 7, 11, 13, 13, 15, 13, 4, 7, 7, 9, 11, 15, 13, 17, 17, 13, 17, 2, 3, 5, 9, 11, 11, 13, 15, 13, 13

Offset: 1

Clark Kimberling, Jan 30 2023

			First seven rows:
  -1
   0    1
   0    3   3
   2    3   5   5
   0    3   3   3   7
   2    3   5   9   7   11
   0    3   7   7   9   11   9
T(4,3) = prime(7) - prime(4) - prime(3) = 17 - 7 - 5 = 5.

Cf. A000040, A066066 (right diagonal).

p[n_] := Prime[n];
t = Table[p[m + n] - p[m] - p[n], {m, 1, 15}, {n, 1, m}]
Flatten[t]    (* A360206 sequence *)
TableForm[t]  (* A360206 array *)

T(m,n) = prime(m+n) - prime(m) - prime(n).

A175509 a(n) = ((2n)-th semiprime) minus 2(n-th semiprime).

Original entry on oeis.org

-2, -2, -3, 2, -2, 4, -4, 2, 1, 5, -4, 1, 7, 9, 9, 1, -3, 9, 8, 7, 7, 9, 11, 5, -2, 4, -3, -1, 6, 11, 12, 16, 17, 19, 2, -5, -11, -10, -1, 7, 10, 16, 9, 12, 21, 13, 15, 16, 15, 22, 11, 10, 11, 13, 9, 17, 7, 9, 11, 12, 17, 6, -4, 3, 7, 7, 15, 27, 21, 25, 28, 35, 37, 43, 43, 41, 31, 31, 20

Offset: 1

Juri-Stepan Gerasimov, Jun 02 2010

sign

			a(1) = -2 because ((2*1)-th semiprime) - 2*(1st semiprime) = 6 - 2*4 = -2.

Cf. A066066.

a(n) = A099981(n) - A075818(n).

Entries checked by R. J. Mathar, Aug 12 2010

A175510 (2n)-th twin prime minus 2(n-th twin prime).

Original entry on oeis.org

-1, 1, 3, 7, 15, 25, 33, 43, 45, 55, 63, 61, 69, 55, 81, 37, 63, 67, 93, 73, 141, 133, 159, 163, 207, 217, 231, 247, 261, 355, 363, 349, 375, 343, 477, 469, 483, 439, 465, 457, 531, 439, 447, 439, 453, 505, 525, 439, 441, 469, 477, 469

Offset: 1

Juri-Stepan Gerasimov, Jun 02 2010

sign

			a(1)=-1 because A001097(2*1)-2*A001097(1)=5-2*3=-1.

Cf. A066066.

a(n)=A001097(2n)-2*A001097(n).

cp's OEIS Frontend

A071186 Numbers k such that prime(2*k)-2*prime(k) is prime.

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A074766 a(n) = prime(2n) - 2*prime(n) - n.

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A230329 Prime(prime(2*n)) - 2*prime(n).

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A360206 Triangular array T(m,n) read by antidiagonals: T(m,n) = prime(m+n) - prime(m) - prime(n).

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A175509 a(n) = ((2*n)-th semiprime) minus 2*(n-th semiprime).

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A175510 (2*n)-th twin prime minus 2*(n-th twin prime).

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A071186 Numbers k such that prime(2k)-2prime(k) is prime.

A230329 Prime(prime(2n)) - 2prime(n).

A175509 a(n) = ((2n)-th semiprime) minus 2(n-th semiprime).

A175510 (2n)-th twin prime minus 2(n-th twin prime).