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%I #19 Sep 09 2017 19:40:05
%S 10,15,25,26,35,38,39,58,65,82,85,87,91,94,118,119,121,123,133,134,
%T 142,143,155,166,183,185,201,202,209,213,217,226,237,253,267,274,278,
%U 287,295,298,299,301,303,305,314,319,321,339,355,362,371,377,381,395,407,413,415,417,422,427
%N Semiprimes having no representation of the form semiprime(n)-+n, where semiprime(n) = A001358(n).
%H Robert Israel, <a href="/A173477/b173477.txt">Table of n, a(n) for n = 1..10000</a>
%e Listing the first eight terms of A001358 gives us:
%e n: 1, 2, 3, 4, 5, 6, 7, 8, ...
%e 4, 6, 9, 10, 14, 15, 21, 22, ...
%e We see that 4 can be represented as 6-2, 6 can be represented as 4+2 or 9-3 or 10-4, 9 can be represented as 14-5 or 15-6, but 10 cannot be represented by any such sum or difference as 4+1, 6+2, 9+3, 14-5, 15-6, 21-7, and also any difference A001358(n)-n after that will miss it. Thus 10 is the first semiprime included in this sequence.
%p N:= 2000: # to use semiprimes <= N
%p Primes:= select(isprime, [2,seq(i,i=3..N,2)]):
%p Semiprimes:= select(`<=`,{seq(seq(Primes[i]*Primes[j],i=1..j),j=1..nops(Primes))},N):
%p sort(convert(Semiprimes minus {seq}(i+Semiprimes[i],i=1..nops(Semiprimes)) minus {seq}(Semiprimes[i]-i,i=1..nops(Semiprimes))),list)); # _Robert Israel_, Dec 20 2015
%Y Cf. A001358, A100493, A172096.
%K nonn,easy
%O 1,1
%A _Juri-Stepan Gerasimov_, Nov 22 2010
%E Corrected by _D. S. McNeil_, Nov 23 2010
%E Name clarified and Example section added by _Antti Karttunen_, Dec 20 2015
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