cp's OEIS Frontend

A371002 a(n) are the records of the number of square addends producing a sequence of consecutive composites starting at A371001(n).

%I A371002 #24 Mar 18 2024 11:45:18
%S A371002 0,2,3,6,8,11,14,17,26,44,68,92,113,128,158,209,224,293,356,401,413,
%T A371002 431,473,584,629,650,743,854,1007,1010,1106,1112,1148,1280,1295,1319,
%U A371002 1358,1364,1388,1616,1643,1664,1799,1859,1973,2000,2162,2234,2294,2393,2501
%N A371002 a(n) are the records of the number of square addends producing a sequence of consecutive composites starting at A371001(n).
%H A371002 Hugo Pfoertner, <a href="/A371002/b371002.txt">Table of n, a(n) for n = 1..56</a>
%e A371002 a(1) = 0: A371001(1) = 4 is the least composite; 4+1^2 = 5 is prime;
%e A371002 a(2) = 2: A371001(2) = 8; 2 composites 8+1^2, 8+2^2; 8+3^2 is prime.
%e A371002 a(3) = 3: A371001(3) = 21; 3 composites 21+1^2, 21+2^2, 21+3^2; 21+4^2 is prime.
%e A371002 a(4) = 6: A371001(4) = 24; 6 composites 24+1^2, 24+2^2, 24+3^3, 24+4^2, 24+5^2, 24+6^2; 24+7^2=73 is prime.
%e A371002 a(51) = 2501 corresponds to A371001(51) = 1470353892839 =
%e A371002 13*59*103*18611839, followed by the 2501 composites 1470353892839+1,
%e A371002 1470353892839+4, ..., 1470353892839+2501^2 = 2^7*3^2*5*23*139*79857;
%e A371002 1470353892839+2502^2 = 1470360152843 is prime.
%o A371002 (PARI) See A371001.
%Y A371002 Cf. A000290, A002808, A371001.
%K A371002 nonn
%O A371002 1,2
%A A371002 _Hugo Pfoertner_, Mar 07 2024
%E A371002 a(45)-a(50) confirmed by data in A371001 from _Martin Ehrenstein_, Mar 08 2024