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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

%I #12 Mar 31 2012 13:22:09

%S 0,1,-1,1,-1,-1,11,7,17,11,-1,-1,11,13,41,-1,41,-1,1,11,-1,-1,17,41,

%T -1,23,97,11,7,47,-1,59,71,1,137,31,97,67,137,119,47,43,101,7,101,91,

%U 43,13,11,31,137,71,49,41,137,47,11,61,67

%N 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.

%C 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.

%H Pierre CAMI, <a href="/A187563/b187563.txt">Table of n, a(n) for n = 1..25000</a>

%t 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}]

%K sign

%O 1,7

%A _Pierre CAMI_, Mar 13 2011

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Last modified August 15 08:18 EDT 2024. Contains 375173 sequences. (Running on oeis4.)