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A084704 Smallest prime p > prime(n) such that (p + prime(n))/2 is prime. 8
7, 17, 19, 23, 61, 29, 43, 59, 53, 43, 97, 53, 79, 59, 89, 83, 73, 79, 107, 181, 127, 131, 113, 109, 113, 151, 167, 193, 149, 151, 167, 197, 163, 197, 163, 229, 199, 179, 281, 347, 241, 263, 229, 257, 223, 271, 331, 239, 313, 269, 263, 313, 263, 269, 359, 293 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Subsidiary sequences: (1) Sequence of primes for a given prime p such that (p+q)/2 is a prime iff q belongs to this sequence. For example, for p = 5 the sequence is 17, 29, 41, 53, 89,...

Note that actually a(n) > prime(n+1) in all cases - because there is no prime between prime(n) and prime(n+1). - Zak Seidov, Jul 24 2013.

LINKS

T. D. Noe and Zak Seidov, Table of n, a(n) for n = 2..10000

MATHEMATICA

Table[p = q = Prime[n]; While[q = NextPrime[q]; ! PrimeQ[(p + q)/2]]; q, {n, 2, 100}] (* T. D. Noe, Apr 20 2011 *)

p=2; Table[p=NextPrime[p]; q=NextPrime[p, 2]; While[!PrimeQ[(p+q)/2], q=NextPrime[q]]; q, {99}] (* Zak Seidov, Jul 24 2013 *)

CROSSREFS

Cf. A001358, A165138.

Sequence in context: A167797 A001913 A071845 * A198032 A175901 A140566

Adjacent sequences:  A084701 A084702 A084703 * A084705 A084706 A084707

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 08 2003

EXTENSIONS

More terms from David Wasserman, Jan 03 2005

STATUS

approved

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Last modified December 21 20:27 EST 2014. Contains 252326 sequences.