cp's OEIS Frontend

A162662 Sequence of alternating increasing odd and increasing even numbers such that the sum of any two terms of opposite parity is a prime number.

%I A162662 #24 Dec 22 2014 17:44:35
%S A162662 1,2,3,4,9,10,27,70,57,100,267,1060,1227,27790,1479,146380,3459,
%T A162662 2508040,49527,35506900,470079
%N A162662 Sequence of alternating increasing odd and increasing even numbers such that the sum of any two terms of opposite parity is a prime number.
%C A162662 a(n+1) is taken to be the smallest number, greater than a(n-2), of opposite parity to a(n) that satisfies the condition.
%C A162662 A000034: Period 2: repeat [1, 2] is another sequence satisfying the definition without the increasing constraint. - _Michel Marcus_, Dec 22 2014
%e A162662 1060 + 267 = 1327 is prime;
%e A162662 1060 + 27 = 1087 is prime;
%e A162662 1060 + 9 = 1069 is prime;
%e A162662 1060 + 3 = 1063 is prime;
%e A162662 1060 + 1 = 1061 is prime.
%p A162662 with(numtheory):nn:=30:T:=array(1..nn): T[1]:=1:a:=1:for k from 2 to nn do:id:=0:for
%p A162662   n from k to 1000000 while(id=0) do:n1:=irem(n,2):i:=0:for p from 1 to a do:
%p A162662   if n=T[p] then i:=0:else fi: x:=n+T[p]:if type(x, prime)=true then i:=i+1:else
%p A162662   fi:od: if i=ceil(a/2) then T[k]:=n:print(n):a:=a+1:id:=1:else fi:od:od:
%o A162662 (PARI) ok(k, m, v) = {if (k % 2, js = 2, js = 1); forstep(j=js, m, 2, if (! isprime(k + v[j]), return (0));); return (1);}
%o A162662 findval(n, v) = {if (n <=2, k = n, k = v[n-2]+2); while (!ok (k, n-1, v), k+= 2); k;}
%o A162662 lista(nn) = {a = vector(nn); a[1] = 1; print1(a[1], ", "); for (n=2, nn, a[n] = findval(n, a); print1(a[n], ", "););} \\ _Michel Marcus_, Dec 22 2014
%Y A162662 Cf. A180743, A115760.
%K A162662 nonn,more
%O A162662 1,2
%A A162662 _Michel Lagneau_, Jan 27 2011
%E A162662 a(18)-a(21) from _Michel Marcus_, Dec 22 2014
%E A162662 Name clarified by _Michel Marcus_, Dec 22 2014