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 A365050 Slowest increasing sequence of primes such that a(n - 1) + a(n) and a(n - 1)^2 + a(n)^2 are both semiprimes, with a(1)=2. 1
 2, 19, 1459, 1699, 3079, 3259, 5419, 5479, 6079, 6679, 7219, 8059, 8719, 11299, 12619, 13219, 13399, 15559, 15679, 18919, 24379, 25219, 26839, 34819, 38239, 39019, 39799, 40459, 40759, 42019, 43399, 44119, 47059, 47779, 54559, 55339, 57139, 60259, 65479, 65599, 68659, 69859, 72559, 77659, 78439 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For n > 1, (a(n - 1) + a(n))/2 and (a(n - 1)^2 + a(n)^2)/2 are primes and a(n) == 19 (mod 60). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(2) = 19 because 2+19=21=3*7 and 2^2+19^2=365=3*73 are semiprimes, and none of the primes from 3 to 17 works. MAPLE R:= 2, 19: p:= 19: count:= 1: q:= 19: while count < 100 do q:= nextprime(q); if isprime((p+q)/2) and isprime((p^2+q^2)/2) then R:= R, q; p:= q; count:= count+1; fi od: R; MATHEMATICA s = {2}; p = 2; Do[q = NextPrime[p]; While[{2, 2} != PrimeOmega[{p + q, p^2 + q^2}], q = NextPrime[q]]; AppendTo[s, p = q], {10}]; s CROSSREFS Cf. A001358. Sequence in context: A369946 A350933 A172028 * A024229 A094663 A274762 Adjacent sequences: A365047 A365048 A365049 * A365051 A365052 A365053 KEYWORD nonn AUTHOR Zak Seidov and Robert Israel, Aug 18 2023 STATUS approved

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Last modified August 10 23:32 EDT 2024. Contains 375059 sequences. (Running on oeis4.)