cp's OEIS Frontend

A370687 a(n) is the first number that is the sum of k successive semiprimes for 1 <= k <= n.

%I A370687 #7 Feb 27 2024 19:36:32
%S A370687 4,10,134,2045,2705,16626281
%N A370687 a(n) is the first number that is the sum of k successive semiprimes for 1 <= k <= n.
%C A370687 a(7) > 5 * 10^8 if it exists.
%e A370687 a(3) = 134 because 134 = 2 * 67 is a semiprime, the sum of two successive semiprimes 65 = 5 * 13 and 69 = 3 * 23, and the sum of three successive semiprimes 39 = 3 * 13, 46 = 2 * 23, 49 = 7 * 7, and is the least such number.
%p A370687 N:= 2*10^7: # for terms <= N
%p A370687 P:= select(isprime, [2, seq(i, i=3..N/2, 2)]):
%p A370687 nP:= nops(P):
%p A370687 SP:= 0:
%p A370687 for i from 1 while P[i]^2 <= N do
%p A370687   m:= ListTools:-BinaryPlace(P, N/P[i]);
%p A370687   SP:= SP, op(P[i]*P[i..m]);
%p A370687 od:
%p A370687 SP:= sort([SP]):
%p A370687 SS:= ListTools:-PartialSums(SP):
%p A370687 V:= Vector(6):
%p A370687 SI:= Vector(6):
%p A370687 II:= Vector(6,1):
%p A370687 for i from 1 to 6 do SI[i]:= SS[i+1]-SS[1] od:
%p A370687 count:= 1: V[1]:= 4: m:= 4: im:= {1}:
%p A370687 while count < 6 do
%p A370687   for j in im do
%p A370687     II[j]:= II[j]+1;
%p A370687     SI[j]:= SS[II[j]+j] - SS[II[j]];
%p A370687   od;
%p A370687   m:= min(SI);
%p A370687   im:= select(j -> SI[j] = m, {$1..20});
%p A370687   for k from 1 to 20 while {$1..k} subset im do
%p A370687     if V[k] = 0 then V[k]:= m; count:= count+1 fi
%p A370687   od;
%p A370687 od:
%p A370687 convert(V,list);
%Y A370687 Cf. A001358, A092192, A370162, A370685.
%K A370687 nonn,more
%O A370687 1,1
%A A370687 _Robert Israel_, Feb 27 2024