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%I
%S 3,7,13,31,89,113,131,449,577,683,743,839,887,1039,1237,1637,1831,
%T 2039,2213,2221,2557,2843,2939,3391,3947,4111,4139,4889,5281,5987,
%U 6803,6841,7883,8513,10667,10739,13381,13487,14177,14563,14639,15319,15443,16273
%N Primes P(n) such that 2*P(n) - P(n+1) has all factors less than P(n+1) - P(n). This means that no prime less than P(n) can divide P(n) to give a remainder added to P(n) to give P(n+1).
%C These primes need not necessarily occur before a large prime gap.
%C Do they occur less frequently than twin primes?
%F Found by inspecting a table of factors and primes.
%e For P(n)=1237 and P(n+1)=1249, 2*1237 - 1249 = 1225 = 5^2 * 7^2
%e and 5,7 < 1249 - 1237 = 12.
%t Join[{3}, Prime[Select[Range[3, 2000], FactorInteger[2*Prime[ # ] - Prime[ # + 1]][[ -1, 1]] < Prime[ # + 1] - Prime[ # ] &]]] (* _Stefan Steinerberger_, Jan 31 2009 *)
%K base,easy,nonn
%O 1,1
%A _J. M. Bergot_, Jan 20 2009
%E Corrected and extended by _Stefan Steinerberger_, Jan 31 2009
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