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 A224489 Smallest k such that k*2*p(n)^2-1 is prime. 9
 1, 1, 3, 1, 1, 1, 1, 4, 4, 6, 4, 6, 1, 1, 9, 10, 1, 6, 4, 7, 1, 4, 3, 4, 3, 10, 4, 4, 1, 1, 1, 10, 1, 7, 6, 12, 1, 9, 6, 3, 1, 1, 6, 3, 1, 1, 1, 3, 3, 4, 4, 21, 4, 1, 3, 1, 6, 4, 1, 10, 3, 1, 15, 1, 3, 4, 9, 13, 10, 9, 1, 4, 1, 3, 1, 3, 12, 9, 6, 1, 1, 22, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Pierre CAMI, Table of n, a(n) for n = 1..10000 EXAMPLE 1*2*2^2-1=7 is prime, p(1)=2 so a(1)=1. 1*2*3^2-1=17 is prime, p(2)=3 so a(2)=1. 1*2*5^2-1=49 is composite; 2*2*5^2-1=99 is composite; 3*2*5^2-1=149 is prime, p(3)=5 so a(3)=3. MATHEMATICA a[n_] := For[k = 1, True, k++, If[ PrimeQ[k*2*Prime[n]^2 - 1], Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 10 2013 *) PROG PFGW and SCRIPTIFY SCRIPT DIM k DIM i, 0 DIM q DIMS t OPENFILEOUT myf, a(n).txt LABEL a SET i, i+1 IF i>50000 THEN END SET k, 0 LABEL b SET k, k+1 SETS t, %d, %d, %d\,; k; i; p(i) SET q, k*2*p(i)^2-1 PRP q, t IF ISPRP THEN WRITE myf, t IF ISPRP THEN GOTO a GOTO b (MAGMA) S:=[]; k:=1; for n in [1..90] do   while not IsPrime(k*2*NthPrime(n)^2-1) do        k:=k+1;   end while;   Append(~S, k);   k:=1; end for; S; // Bruno Berselli, Apr 18 2013 CROSSREFS Cf. A224490, A224491, A224492. Sequence in context: A122947 A231147 A046534 * A318933 A140334 A131324 Adjacent sequences:  A224486 A224487 A224488 * A224490 A224491 A224492 KEYWORD nonn AUTHOR Pierre CAMI, Apr 08 2013 STATUS approved

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Last modified April 5 10:28 EDT 2020. Contains 333239 sequences. (Running on oeis4.)