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 A085956 Smallest prime p such that (2n)*p +1 and (p-1)/(2n) are prime, or 0 if no such prime exists. 7
 5, 13, 13, 17, 31, 61, 239, 0, 127, 41, 0, 73, 131, 0, 61, 1889, 0, 397, 419, 0, 211, 89, 0, 97, 101, 0, 163, 113, 0, 181, 2543, 0, 463, 2789, 211, 5689, 149, 0, 547, 881, 0, 1093, 173, 0, 271, 9293, 0, 673, 491, 0, 1123, 14249, 0, 10909, 3191, 0, 229, 1973, 0, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes of the form 16*p + 1 == {1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91} (mod 96). With rare exceptions, a(3n-1)=0. a(2)=13, a(5)=31 and a(35)=211, all of which are of the form 6n+1. This is true for those 6317 n's which have a solutions less than 10^6. I have no proof! - Robert G. Wilson v LINKS EXAMPLE a(5) = 31 as (2*5)*31 + 1= 311 as well as (31-1)/10 = 3 are primes. MATHEMATICA f[n_] := Block[{k = 1}, While[k < 10^12 && ( !PrimeQ[k] || !PrimeQ[2*n*k + 1] || !PrimeQ[(k - 1)/(2n)] ), k += 2n]; If[k >= 10^12, 0, k]]; Table[ f[n], {n, 1, 61}] CROSSREFS Sequence in context: A274302 A274300 A051899 * A232610 A235337 A151994 Adjacent sequences:  A085953 A085954 A085955 * A085957 A085958 A085959 KEYWORD nonn AUTHOR Amarnath Murthy, Jul 16 2003 EXTENSIONS Corrected by Labos Elemer, Jul 17 2003 Edited and extended by Robert G. Wilson v, Jul 18 2003 STATUS approved

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Last modified July 1 16:51 EDT 2022. Contains 354973 sequences. (Running on oeis4.)