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 A212037 The size of the set of numbers k>=0 such that all (2^n+k)*2^n-1 are prime but only the last (largest) (2^n+k)*2^n+1 is also an associated twin prime. 5
 1, 6, 1, 4, 2, 2, 2, 24, 6, 2, 28, 7, 16, 47, 29, 6, 41, 16, 3, 17, 32, 10, 10, 23, 14, 15, 52, 4, 13, 20, 23, 4, 84, 26, 88, 50, 20, 35, 51, 44, 41, 87, 1, 142, 13, 188, 107, 162, 91, 96, 197, 4, 148, 71, 9, 66, 97, 41, 10, 9, 152, 234, 48, 104, 144, 40, 18, 45, 52, 204, 21, 49, 51, 9, 102, 13, 31, 108, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Starting at a count of zero, we consider for increasing k>=0 the pairs (2^n+k)*2^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime. Heuristically, the average of a(n)/n over n=1 to N tends to 1 as N increases. LINKS Pierre CAMI, Table of n, a(n) for n = 1..825 EXAMPLE For n=2, the 6 pairs (19,21) at k=1, (23,25) at k=2, (31,33) at k=4, (43,45) at k=7, (47,49) at k=8 and (59,61) at k=11 are counted. The smaller of these must be a prime to be counted, and at k=11 also the larger (ie, 61) becomes prime, which finishes the search. MAPLE A212037 := proc(n)     local a, k, p ;     a := 0 ;     for k from 0 do         p := (2^n+k)*2^n-1 ;         if isprime(p) then             a := a+1 ;         end if;         if isprime(p) and isprime(p+2) then             return a;         end if;     end do: end proc: # R. J. Mathar, Jul 20 2012 PROG SCRIPT DIM nn, 0 DIM jj DIM kk DIMS tt OPENFILEOUT myfile, a(n).txt LABEL loopn SET nn, nn+1 IF nn>825 THEN END SET kk, -1 SET jj, 0 LABEL loopk SET kk, kk+1 SETS tt, %d, %d\,; nn; kk PRP (2^nn+kk)*2^nn-1, tt IF ISPRP THEN GOTO a IF ISPRIME THEN GOTO a GOTO loopk LABEL a SET jj, jj+1 PRP (2^nn+kk)*2^nn+1, tt IF ISPRP THEN GOTO d IF ISPRIME THEN GOTO d GOTO loopk LABEL d SETS tt, %d, %d\,; nn; jj WRITE myfile, tt GOTO loopn CROSSREFS Cf. A191617, A191218, A205321. Sequence in context: A178646 A144540 A292107 * A118740 A301431 A200302 Adjacent sequences:  A212034 A212035 A212036 * A212038 A212039 A212040 KEYWORD nonn AUTHOR Pierre CAMI, Jul 14 2012 STATUS approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)