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 A351051 a(n) is the least prime that begins a sequence of exactly n primes under iteration of the map x -> (x^2+2)/3. 0
 3, 11, 17, 7, 25781659, 13505561767 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..6. EXAMPLE 7 is prime, (7^2+2)/3 = 17 is prime, (17^2+2)/3 = 97 is prime, (97^2+2)/3 = 3137 is prime, but (3137^2+2)/3 = 3280257 is not prime, so 7 begins the sequence of 4 primes (7, 17, 97, 3137). Since this is the first prime to do so, a(4) = 7. MAPLE f:= proc(p) option remember; local q; q:= (p^2+2)/3; if isprime(q) then 1 + procname(q) else 1 fi end proc: A:= Vector(5): count:= 0: p:= 3: while count < 5 do p:= nextprime(p); v:= f(p); if A[v] = 0 then A[v]:= p; count:= count+1; fi; od: convert(A, list); MATHEMATICA f[n_] := -1 + Length @ NestWhileList[(#^2 + 2)/3 &, n, PrimeQ]; a[n_] := Module[{p = 3}, While[f[p] != n, p = NextPrime[p]]; p]; Array[a, 4] (* Amiram Eldar, Feb 01 2022 *) CROSSREFS Cf. A109953. Sequence in context: A298701 A216911 A356074 * A154497 A322171 A038946 Adjacent sequences: A351048 A351049 A351050 * A351052 A351053 A351054 KEYWORD nonn,more AUTHOR J. M. Bergot and Robert Israel, Jan 30 2022 EXTENSIONS a(6) from Amiram Eldar, Feb 01 2022 STATUS approved

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Last modified June 8 11:34 EDT 2023. Contains 363164 sequences. (Running on oeis4.)