A371002 - OEIS

%I #24 Mar 18 2024 11:45:18

%S 0,2,3,6,8,11,14,17,26,44,68,92,113,128,158,209,224,293,356,401,413,

%T 431,473,584,629,650,743,854,1007,1010,1106,1112,1148,1280,1295,1319,

%U 1358,1364,1388,1616,1643,1664,1799,1859,1973,2000,2162,2234,2294,2393,2501

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

%H Hugo Pfoertner, <a href="/A371002/b371002.txt">Table of n, a(n) for n = 1..56</a>

%e a(1) = 0: A371001(1) = 4 is the least composite; 4+1^2 = 5 is prime;

%e a(2) = 2: A371001(2) = 8; 2 composites 8+1^2, 8+2^2; 8+3^2 is prime.

%e a(3) = 3: A371001(3) = 21; 3 composites 21+1^2, 21+2^2, 21+3^2; 21+4^2 is prime.

%e 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 a(51) = 2501 corresponds to A371001(51) = 1470353892839 =

%e 13*59*103*18611839, followed by the 2501 composites 1470353892839+1,

%e 1470353892839+4, ..., 1470353892839+2501^2 = 2^7*3^2*5*23*139*79857;

%e 1470353892839+2502^2 = 1470360152843 is prime.

%o (PARI) See A371001.

%Y Cf. A000290, A002808, A371001.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Mar 07 2024

%E a(45)-a(50) confirmed by data in A371001 from _Martin Ehrenstein_, Mar 08 2024