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%I #18 Oct 15 2016 08:00:37
%S 1,3,5,11,17,23,25,27,29,41,59,61,71,97,99,101,107,125,137,147,149,
%T 167,169,171,179,191,197,227,229,231,239,241,269,277,279,281,311,347,
%U 387,397,399,419,421,431,461,521,539,567,569,599,601,617,625,639,641
%N Lesser of pairs of odd numbers (n, n+2) such that the product of invertible quadratic residues == (n+1)(-1)^((n+1)/2) (modulo n(n+2)).
%C Twin primes satisfy the same property, so A001359 is included in this sequence.
%H Christian Aebi and Grant Cairns, <a href="http://www.emis.de/journals/INTEGERS/papers/m7/m7.Abstract.html">A property of twin primes,</a> Integers 12(2012), A7.
%o (PARI) isptp (p) = {local(pq); pq = p*(p+2); if (prod(x=1, pq, if (issquare(Mod(x, pq)) && (gcd(x, pq) == 1), x, 1)) % pq == ((p+1) * ((-1)^((p+1)/2))) % pq , return(1), return(0));} allptp(n) = {local(i, p, q); p = []; q = []; forstep (i=1, n, 2, if (isptp(i), p = concat(p, i); q = concat(q, i+2););); print(p); print(q);}
%Y Cf. A001359, A006512, A001097.
%K nonn
%O 1,2
%A _Michel Marcus_, Sep 05 2012
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