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 A187866 Greatest k such that prime(n)*(prime(n)-k)-1 and prime(n)*(prime(n)-k)+1 are twin primes, k >= 0 and k < prime(n) or -1 if no such k exists. 1
 0, 1, -1, 1, -1, -1, 11, 7, 17, 17, -1, -1, 11, 19, 41, -1, 41, -1, 43, 53, -1, -1, 29, 41, -1, 59, 97, 101, 61, 89, -1, 101, 131, 127, 137, 73, 133, 127, 137, 119, 47, 163, 101, 157, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Conjectures: 1. There are only 11 primes such that k does not exist: 5, 11, 13, 31, 37, 53, 61, 73, 79, 97, 127 (same as A183563). 2. There are only 20 primes such that k(n) = A187563(n): 2, 3, 7, 17, 19, 23, 41, 47, 59, 89, 103, 149, 167, 173, 179, 191, 277, 353, 433, 727. 3. If prime(n) >= 3 there are always at least 2 pairs of twin primes between prime(n) and prime(n)^2. LINKS Pierre CAMI, Table of n, a(n) for n = 1..25000 MATHEMATICA a[n_] := (k=Prime[n]-1; While[p = Prime[n]*(Prime[n]-k)-1; k>=0 && !(PrimeQ[p] && PrimeQ[p + 2]), k--]; k); a /@ Range[45] (* Jean-François Alcover, Mar 28 2011 *) PROG (PFGW SCRIPTIFY) SCRIPT DIM nn, 1 DIM kk DIMS tt OPENFILEOUT out, twin LABEL loopn SET nn, nn+1 IF nn>25000 THEN END SET kk, p(nn) LABEL loopk SET kk, kk-2 IF kk==-1 THEN GOTO c SETS tt, %d, %d, %d\,; nn; p(nn); kk PRP p(nn)*(p(nn)-kk)-1, tt IF ISPRIME THEN GOTO a GOTO loopk LABEL a PRP p(nn)*(p(nn)-kk)+1, tt IF ISPRIME THEN GOTO b GOTO loopk LABEL b WRITE out, tt GOTO loopn LABEL c SET kk, -1 SETS tt, %d, %d, %d\,; nn; p(nn); kk WRITE out, tt GOTO loopn CROSSREFS Cf. A187563. Sequence in context: A187563 A089487 A166521 * A206419 A250032 A305447 Adjacent sequences: A187863 A187864 A187865 * A187867 A187868 A187869 KEYWORD sign AUTHOR Pierre CAMI, Mar 14 2011 STATUS approved

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