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 A210650 Least number k>0 such that at least one of (2^k-1)*2^n-1, (2^k-1)*2^n+1, (2^k+1)*2^n-1, or (2^k+1)*2^n+1 is a prime number. 1
 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 3, 5, 5, 7, 2, 3, 4, 5, 3, 1, 1, 2, 3, 1, 5, 1, 4, 1, 2, 8, 1, 3, 1, 4, 3, 5, 5, 2, 17, 3, 4, 3, 21, 2, 1, 5, 8, 10, 7, 4, 1, 12, 3, 1, 3, 1, 3, 5, 8, 10, 8, 2, 4, 20, 2, 1, 11, 4, 14, 4, 3, 4, 17, 12, 2, 8, 13, 7, 1, 13, 5, 3, 5, 1, 8, 4, 13, 6, 3, 21, 10, 5, 1, 12, 7, 5, 1, 12, 3, 9, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS More than 73% of a(n) are < n/10. Conjecture: for n>1 a(n) is always < n. Define partial sums S(N) = sum_{i=1..N} a(i) and T(N)=sum_{i=1..N} i = A000217(N). Then as N increases S(N)/T(n) tends to 0.078. LINKS Pierre CAMI, Table of n, a(n) for n = 1..10000 MAPLE A210650 := proc(n)         for k from 1 do                 if isprime((2^k-1)*2^n-1) then                         return k;                 elif isprime((2^k-1)*2^n+1) then                         return k;                 elif isprime((2^k+1)*2^n-1) then                         return k;                 elif isprime((2^k+1)*2^n+1) then                         return k;                 end if;         end do: end proc: # R. J. Mathar, Apr 02 2012 MATHEMATICA lnk[n_]:=Module[{k=1, t=2^n}, While[!AnyTrue[Flatten[{t(2^k-1)+{1, -1}, t(2^k+1)+ {1, -1}}], PrimeQ], k++]; k]; Array[lnk, 120] (* The program uses the AnyTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 31 2015 *) PROG PFGW64 and SCRIPTIFY from Primeform group Command: PFGW64 -f in.txt in.txt file : SCRIPT DIM nn, 0 DIM kk DIMS tt OPENFILEOUT myfile, a(n).txt LABEL loopn SET nn, nn+1 IF nn>10000 THEN END SET kk, 0 LABEL loopk SET kk, kk+1 IF kk>2*nn THEN GOTO loopn SETS tt, %d, %d, %d, %d\,; nn; kk; -1; -1 PRP 2^nn*(2^kk-1)-1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a SETS tt, %d, %d, %d, %d\,; nn; kk; -1; 1 PRP 2^nn*(2^kk-1)+1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a SETS tt, %d, %d, %d, %d\,; nn; kk; 1; -1 PRP 2^nn*(2^kk+1)-1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a SETS tt, %d, %d, %d, %d\,; nn; kk; 1; 1 PRP 2^nn*(2^kk+1)+1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a GOTO loopk LABEL a WRITE myfile, tt GOTO loopn CROSSREFS Sequence in context: A073356 A093032 A072115 * A218754 A079948 A257657 Adjacent sequences:  A210647 A210648 A210649 * A210651 A210652 A210653 KEYWORD nonn AUTHOR Pierre CAMI, Mar 27 2012 STATUS approved

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Last modified July 29 14:43 EDT 2021. Contains 346346 sequences. (Running on oeis4.)