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%I #6 Mar 30 2012 18:36:00
%S 2,23,29,41,47,83,113,163,167,173,191,223,233,251,257,263,269,293,307,
%T 337,347,353,373,383,419,461,503,587,593,599,631,659,673,683,719,761,
%U 797,839,853,881,1009,1013,1049,1091,1129,1163,1187,1217,1259,1283,1289
%N Primes p such that all p-k!! are composite for 1<=k!!<p.
%e 29 is in the sequence because :
%e 29 - 0!! = 29 - 1 = 28;
%e 29 - 1!! = 29 - 1 = 28;
%e 29 - 2!! = 29 - 2 = 27;
%e 29 - 3!! = 29 - 3 = 26;
%e 29 - 4!! = 29 - 8 = 21;
%e 29 - 5!! = 29 - 15 = 14 is the last composite because 6!! = 48 > 29.
%p with(numtheory): for n from 1 to 250 do:p:=ithprime(n):i:=0:for k from 0 to p while (doublefactorial(k)<p) do:x:=p - doublefactorial(k):if type(x,prime)=true then i:=1:else fi:od:if i=0 then printf(`%d, `,p):else fi:od:
%Y Cf. A064152, A006882.
%K nonn,easy
%O 0,1
%A _Michel Lagneau_, Feb 25 2012
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