A217622 -id:A217622 - cp's OEIS frontend

A230460 Prime(2*prime(n)).

7, 13, 29, 43, 79, 101, 139, 163, 199, 271, 293, 373, 421, 443, 491, 577, 647, 673, 757, 821, 839, 929, 983, 1061, 1181, 1231, 1277, 1307, 1361, 1429, 1609, 1667, 1759, 1789, 1973, 1997, 2083, 2161, 2243, 2339, 2411, 2441, 2633, 2663, 2707, 2729, 2917

Offset: 1

M. F. Hasler, Oct 19 2013

A subsequence of A031378 (subsequence of A031215) and of A106349, which are both subsequences of A007821 which is the complement of A006450 in the primes A000040.

			a(3) = 29 because the third prime is 5, and 2 * 5 = 10, and then we see that the tenth prime is 29.
a(4) = 43 because the fourth prime is 7, and 2 * 7 = 14, and then we see that the fourteenth prime is 43.

M. F. Hasler, Table of n, a(n) for n = 1..1000

Cf. A217622.

Prime[2Prime[Range[50]]] (* Alonso del Arte, Oct 19 2013 *)

PARI
```
A230460=n->prime(2*prime(n))
```

a(n) ~ 2n log(n) log(2n log(n)) ~ 2n (log n)^2.

a(n) = A000040(A100484(n)). - Omar E. Pol, Oct 19 2013

A230481 a(n) = prime(prime(2n)) - prime(2prime(n)).

Original entry on oeis.org

-2, 4, 12, 24, 30, 56, 52, 78, 84, 82, 108, 88, 126, 144, 126, 162, 150, 204, 210, 210, 248, 242, 234, 348, 266, 268, 320, 362, 380, 394, 304, 396, 340, 480, 378, 420, 466, 486, 476, 464, 498, 578, 476, 566, 592, 678, 600, 456, 524, 660, 714, 742, 768, 756

Offset: 1

M. F. Hasler, Oct 20 2013

sign

As difference of two odd primes, all terms are even.

M. F. Hasler, Table of n, a(n) for n = 1..10000

Cf. A066066, A000040, A006450, A031215, A217622, A230460.

a=n->prime(prime(2*n))-prime(2*prime(n))

a(n) = A217622(n) - A230460(n) = 2*A230482(n).

A230482 a(n) = (prime(prime(2n)) - prime(2prime(n)))/2.

Original entry on oeis.org

-1, 2, 6, 12, 15, 28, 26, 39, 42, 41, 54, 44, 63, 72, 63, 81, 75, 102, 105, 105, 124, 121, 117, 174, 133, 134, 160, 181, 190, 197, 152, 198, 170, 240, 189, 210, 233, 243, 238, 232, 249, 289, 238, 283, 296, 339, 300, 228, 262, 330, 357, 371, 384, 378, 372

Offset: 1

M. F. Hasler, Oct 20 2013

sign

As difference of two odd primes, all terms of A230481(n) = prime(prime(2*n))-prime(2*prime(n)) are even, which motivates to define the present sequence.

Further values: a(100)=617, a(10^3)=9344, a(10^4)=114171, a(10^5)=1325772, a(10^6)=14979156; a(10^10)~2.2*10^11, a(10^20)~3.9*10^21, a(10^30)~5.5*10^31.

M. F. Hasler, Table of n, a(n) for n = 1..10000

Cf. A066066, A000040, A006450, A031215, A217622, A230460.

a=n->(prime(prime(2*n))-prime(2*prime(n)))/2

a(n) = (A217622(n) - A230460(n))/2.

A228529 a(n) = prime(n*prime(n)).

Original entry on oeis.org

3, 13, 47, 107, 257, 397, 653, 881, 1279, 1889, 2293, 3119, 3847, 4423, 5323, 6563, 7937, 8819, 10391, 11833, 12889, 14831, 16477, 18713, 21599, 23603, 25189, 27409, 29063, 31511, 37159, 39869, 43321, 45589, 50923, 53281, 57271, 61561, 65173, 69821, 74383

Offset: 1

Omar E. Pol, Oct 20 2013

nonn

			For n = 2, prime(2*prime(2)) = prime(2*3) = prime(6) = 13, so a(2) = 13.

Cf. A000040, A006450, A033286, A036689, A080697, A217622, A230098, A230325, A230285, A230460.

Table[Prime[n*Prime[n]], {n, 100}] (* T. D. Noe, Oct 22 2013 *)

a(n) = prime(n*prime(n)); \\ Michel Marcus, Oct 22 2013

a(n) = A000040(A033286(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

cp's OEIS Frontend

A230460 Prime(2*prime(n)).

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A230481 a(n) = prime(prime(2*n)) - prime(2*prime(n)).

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A230482 a(n) = (prime(prime(2*n)) - prime(2*prime(n)))/2.

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A228529 a(n) = prime(n*prime(n)).

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

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A230481 a(n) = prime(prime(2n)) - prime(2prime(n)).

A230482 a(n) = (prime(prime(2n)) - prime(2prime(n)))/2.

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