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A210497
a(n) = 2*prime(n+1) - prime(n).
5
4, 7, 9, 15, 15, 21, 21, 27, 35, 33, 43, 45, 45, 51, 59, 65, 63, 73, 75, 75, 85, 87, 95, 105, 105, 105, 111, 111, 117, 141, 135, 143, 141, 159, 153, 163, 169, 171, 179, 185, 183, 201, 195, 201, 201, 223, 235, 231, 231, 237, 245, 243, 261, 263, 269, 275, 273, 283
OFFSET
1,1
COMMENTS
The subsequence of multiples of 3 begins: 9, 15, 15, 21, 21, 27, 33, 45.
The subsequence of primes begins: 7, 43, 73, 163, 179, 223.
Some terms, like a(3)=15 or a(5)=21, are repeated twice, other terms, like a(23)=105, are repeated three times.
LINKS
Bruno Berselli and Zak Seidov, Table of n, a(n) for n = 1..10000 (a(1)-a(1000) from Bruno Berselli).
FORMULA
a(n) ~ n log n. - Charles R Greathouse IV, Jan 24 2013
EXAMPLE
a(2) = 7 because prime(3) = 5, prime(2) = 3, and 2 * 5 - 3 = 7.
a(3) = 9 because prime(4) = 7, prime(3) = 5, and 2 * 7 - 5 = 9.
a(4) = 15 because prime(5) = 11, prime(4) = 7, and 2 * 11 - 7 = 15.
MATHEMATICA
Table[2 Prime[n + 1] - Prime[n], {n, 50}] (* Vincenzo Librandi, May 03 2015 *)
ListConvolve[{2, -1}, Prime[Range[100]]] (* Paolo Xausa, Oct 29 2024 *)
PROG
(PARI) a(n)=my(p=prime(n)); 2*nextprime(p+1)-p \\ Charles R Greathouse IV, Jan 24 2013
(Magma) [2*NextPrime(p)-p: p in PrimesUpTo(300)]; // Bruno Berselli, Jan 24 2013
(Python)
from sympy import prime, nextprime
def A210497(n): return -(p:=prime(n))+(nextprime(p)<<1) # Chai Wah Wu, Oct 29 2024
CROSSREFS
Cf. A001223, A062234, A085704 (subsequence).
Sequence in context: A287559 A032778 A282058 * A010383 A010403 A032709
KEYWORD
nonn,easy
AUTHOR
Marco Piazzalunga, Jan 24 2013
STATUS
approved