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 A245441 a(1)=3, then a(n) = smallest odd k > Ceiling(a(n-1)/2) such that k*2^n-1 is prime. 2
 3, 3, 3, 3, 7, 17, 13, 27, 25, 15, 25, 23, 21, 15, 9, 17, 15, 21, 51, 35, 19, 33, 25, 39, 57, 57, 81, 45, 45, 213, 111, 57, 31, 131, 99, 83, 45, 27, 25, 107, 55, 33, 33, 35, 67, 141, 91, 89, 69, 41, 129, 89, 147, 101, 195, 129, 79, 77, 45, 77, 69, 53, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A126715(n) = smallest odd k such that k*2^n-1 is prime, the primes are not always in increasing order. Here the primes k*2^n-1 are always in increasing order. The ratio sum_{1..N}a(n)/sum_{1..N}n is near 2*log(2) as N increases. The ratio a(n)/n is always < 8 for n from 1 to 6000. LINKS Pierre CAMI, Table of n, a(n) for n = 1..6000 EXAMPLE 3*2^1-1 = 5 is prime, a(1)=3 by definition. 3*2^2-1 = 11 is prime, 3 > 3/2 so a(2) = 3. 3*2^3-1 = 23 is prime, so a(3) = 3. 3*2^4-1 = 47 is prime, so a(4) = 3. 3*2^5-1 = 95 is composite. 5*2^5-1 = 159 is composite. 7*2^5-1 = 223 is prime so a(5) = 7. PROG (PFGW & SCRIPT) SCRIPT DIM j, -1 DIM n, 0 DIMS t OPENFILEOUT myf, a(n).txt LABEL loop1 SET n, n+1 IF n>6000 THEN END LABEL loop2 SET j, j+2 SETS t, %d, %d\,; n; j PRP j*2^n-1, t IF ISPRP THEN GOTO a GOTO loop2 LABEL a WRITE myf, t SET j, j/2 IF j%2==0 THEN SET j, j+1 GOTO loop1 (PARI) a=[3]; for(n=2, 100, k=floor(a[n-1]/2)+2; if(k%2==0, k++); t=2^n; while(!isprime(k*t-1), k+=2); a=concat(a, k)); a \\ Colin Barker, Jul 22 2014 CROSSREFS Cf. A126715. Sequence in context: A242715 A078229 A222292 * A333793 A007428 A184099 Adjacent sequences:  A245438 A245439 A245440 * A245442 A245443 A245444 KEYWORD nonn AUTHOR Pierre CAMI, Jul 22 2014 STATUS approved

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Last modified October 25 01:18 EDT 2020. Contains 338010 sequences. (Running on oeis4.)