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 A187563 Least k >=0 and k < prime(n) such that prime(n)*(prime(n)-k)-1 and prime(n)*(prime(n)-k)+1 are twin primes or -1 if no such k exists. 2
 0, 1, -1, 1, -1, -1, 11, 7, 17, 11, -1, -1, 11, 13, 41, -1, 41, -1, 1, 11, -1, -1, 17, 41, -1, 23, 97, 11, 7, 47, -1, 59, 71, 1, 137, 31, 97, 67, 137, 119, 47, 43, 101, 7, 101, 91, 43, 13, 11, 31, 137, 71, 49, 41, 137, 47, 11, 61, 67 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Conjectures: there are only 11 primes (5,11,13,31,37,53,61,73,79,97,127) for which k does not exist and there is always at least a pair of twin primes between prime(n) and prime(n)^2. LINKS Pierre CAMI, Table of n, a(n) for n = 1..25000 MATHEMATICA Table[k = 0; While[k < Prime[n] && ! (PrimeQ[Prime[n]*(Prime[n] - k) - 1] && PrimeQ[Prime[n]*(Prime[n] - k) + 1]), k++]; If[k == Prime[n], k = -1]; k, {n, 100}] CROSSREFS Sequence in context: A110093 A282345 A265765 * A089487 A166521 A187866 Adjacent sequences: A187560 A187561 A187562 * A187564 A187565 A187566 KEYWORD sign AUTHOR Pierre CAMI, Mar 13 2011 STATUS approved

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Last modified July 18 17:38 EDT 2024. Contains 374388 sequences. (Running on oeis4.)