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A096476
a(n) = prime(A096475(n)).
2
5, 59, 31, 179, 353, 547, 109, 4133, 6841, 773, 9293, 3733, 10559, 17627, 108643, 9973, 32261, 3259, 22811, 18617, 65731, 60821, 156371, 404029, 55733, 40637, 540619, 192677, 290897, 118297, 693877, 406883, 812527, 264659, 1022303, 928471
OFFSET
3,1
COMMENTS
b(n) = A096475(n) is the smallest (lesser twin) prime such that A096475(n) = 2n. For terms (= a(n) = A096476(n)) of the present sequence, both a(n) and 2n + a(n) are primes; furthermore, a(n) = prime(A096475(n)), i.e., PrimePi(a(n)) = A094475(n); also, a(n) + 2n is not necessarily the next prime after a(n).
FORMULA
a(n) = A000040(A096475(n)).
EXAMPLE
a(6) = 179 is a prime and 2*6 + 179 = 12 + 179 = 191 is also a prime, while pi(191) = 43, pi(179) = 41 are twin primes and 179 is the 6th term of A096475 (offset = 3!).
MATHEMATICA
{ta=Table[0, {1300}], tb=Table[0, {1300}], tc=Table[0, {1300}], u=1}; Do[s=Prime[n+1]-Prime[n]; If[Equal[s, 2], ta[[u]]=Prime[Prime[n+1]]-Prime[Prime[n]]; tb[[u]]=n; tc[[u]]=Prime[n]; td[[u]]=Prime[Prime[n]]; u=u+1], {n, 1, 10000}]; td
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 23 2004
STATUS
approved