cp's OEIS Frontend

A243625 a(n) is the smallest positive integer not already in the sequence for which a(n)+a(n-1) is a semiprime, with a(1)=1.

%I A243625 #21 Feb 23 2017 23:20:02
%S A243625 1,3,6,4,2,7,8,13,9,5,10,11,14,12,21,17,16,18,15,19,20,26,23,28,27,22,
%T A243625 24,25,30,32,33,29,36,38,31,34,35,39,43,42,40,37,45,41,44,47,46,48,58,
%U A243625 53,62,49,57,54,52,59,56,50,61,60,51,55,63,66,67,74,68
%N A243625 a(n) is the smallest positive integer not already in the sequence for which a(n)+a(n-1) is a semiprime, with a(1)=1.
%C A243625 It is probable that every positive integer occurs, and that this is a permutation of natural numbers.
%C A243625 a(n) = n for n = 1, 4, 9, 18, 23, 48, 54, 60, 63, 77, 91, 92, .... (375 cases for first 3000 terms). - _Zak Seidov_, Feb 22 2017
%H A243625 Robert Israel, <a href="/A243625/b243625.txt">Table of n, a(n) for n = 1..10000</a>
%e A243625 a(3)=6 because 1 and 3 have already been used in the sequence and 3+2=5, 3+4=7 and 3+5=8 are not semiprime while 3+6=9 is semiprime.
%p A243625 N:= 1000; # to get all terms up to a(N)
%p A243625 issp:= proc(n) local F; F:= ifactors(n)[2]; add(f[2],f=F)=2 end proc:
%p A243625 S:= {1}; m:= 1; R:= {}; a[1]:= 1;
%p A243625 for n from 2 to N do
%p A243625   found:= false;
%p A243625   for k in R do
%p A243625     if issp(a[n-1]+k) then
%p A243625       a[n]:= k;
%p A243625       S:= S union {k};
%p A243625       R:= R minus {k};
%p A243625       found:= true;
%p A243625       break
%p A243625     fi;
%p A243625   od;
%p A243625   if not found then
%p A243625     for k from m+1 do
%p A243625       if issp(a[n-1]+k) then
%p A243625         a[n]:= k;
%p A243625         S:= S union {k};
%p A243625         R:= R union {$(m+1)..(k-1)};
%p A243625         m:= k;
%p A243625         break
%p A243625       fi
%p A243625     od
%p A243625   fi
%p A243625 od:
%p A243625 seq(a(n),n=1..N); # _Robert Israel_, Jun 08 2014
%t A243625 f[s_List] := Block[{k = 1, a = s[[ -1]]}, While[ MemberQ[s, k] || ! Plus@@Last/@FactorInteger[a+k] == 2, k++ ]; Append[s, k]]; Nest[f, {1}, 71]
%Y A243625 Cf. A055265.
%K A243625 nonn
%O A243625 1,2
%A A243625 _Michel Lagneau_, Jun 08 2014