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

1,2

Links

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

Example

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.

Prog

(PARI) See A371001.

Crossrefs

Cf. A000290, A002808, A371001.

Sequence in context: A097383 A072893 A349662 * A127758 A185599 A211519

Adjacent sequences: A370999 A371000 A371001 * A371003 A371004 A371005

Keyword

nonn

Author

Hugo Pfoertner, Mar 07 2024

Extensions

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

Status

approved