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

0, 2, 3, 6, 8, 11, 14, 17, 26, 44, 68, 92, 113, 128, 158, 209, 224, 293, 356, 401, 413, 431, 473, 584, 629, 650, 743, 854, 1007, 1010, 1106, 1112, 1148, 1280, 1295, 1319, 1358, 1364, 1388, 1616, 1643, 1664, 1799, 1859, 1973, 2000, 2162, 2234, 2294, 2393, 2501

Offset: 1

Author

Hugo Pfoertner, Mar 07 2024

Keywords

• nonn

Examples

			a(1) = 0: A371001(1) = 4 is the least composite; 4+1^2 = 5 is prime;
a(2) = 2: A371001(2) = 8; 2 composites 8+1^2, 8+2^2; 8+3^2 is prime.
a(3) = 3: A371001(3) = 21; 3 composites 21+1^2, 21+2^2, 21+3^2; 21+4^2 is prime.
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.
a(51) = 2501 corresponds to A371001(51) = 1470353892839 =
13*59*103*18611839, followed by the 2501 composites 1470353892839+1,
1470353892839+4, ..., 1470353892839+2501^2 = 2^7*3^2*5*23*139*79857;
1470353892839+2502^2 = 1470360152843 is prime.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..56

Crossrefs

Cf. A000290, A002808, A371001.

Programs

PARI

See A371001.

Extensions

a(45)-a(50) confirmed by data in A371001 from Martin Ehrenstein, Mar 08 2024