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 A358656 Least prime p such that p^n + 2 is the product of n distinct primes. 2
 3, 2, 7, 71, 241, 83, 157, 6947, 4231, 35509, 15541, 199499, 649147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Corresponding values of p^n + 2 are 5, 6, 345, 25411683, 812990017203, 326940373371, 2351243277537495, ... LINKS Table of n, a(n) for n=1..13. EXAMPLE a(1) = 3; 3^1 + 2 = 5. a(2) = 2; 2^2 + 2 = 2 * 3. a(3) = 7; 7^3 + 2 = 3 * 5 * 23. a(4) = 71; 71^4 + 2 = 3 * 11 * 19 * 40529. MATHEMATICA Table[b=2; y[a_]:=FactorInteger[Prime[a]^n+b]; k=1; Monitor[Parallelize[While[True, If[And[Length[y[k]]==n, Count[Flatten[y[k]], 1]==n], Break[]]; k++]; k], k]//Prime, {n, 1, 10}] PROG (PARI) a(n) = forprime(p=2, , my(f=factor(p^n + 2)); if (issquarefree(f) && (omega(f) == n), return(p))); \\ Michel Marcus, Nov 29 2022 CROSSREFS Cf. A280005, A000961, A005117. Sequence in context: A363400 A230710 A265009 * A021757 A143312 A224234 Adjacent sequences: A358653 A358654 A358655 * A358657 A358658 A358659 KEYWORD nonn,more AUTHOR J.W.L. (Jan) Eerland, Nov 27 2022 EXTENSIONS a(13) from Daniel Suteu, Dec 09 2022 STATUS approved

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Last modified June 15 09:26 EDT 2024. Contains 373407 sequences. (Running on oeis4.)