%I #22 Feb 24 2023 07:16:01

%S 2,1,2,4,5,3,5,3,6,8,6,9,5,3,9,3,8,6,12,8,6,13,9,3,9,5,3,14,12,8,10,6,

%T 17,15,5,3,15,9,5,18,12,10,20,18,14,12,21,9,5,3,21,15,13,3,20,14,8,6,

%U 24,20,18,8,19,15,13,9,21,15,5,3,26,20,12,6

%N a(n) = number of the column of (R(i,j)) that contains prime(n), where R(i,j) is the rectangle with antidiagonals 1; 2,3; 4,5,6; ...

%C The rectangle R(i,j) has this corner:

%C 1, 2, 4, 7, 11, 16, 22, 29, ...

%C 3, 5, 8, 12, 17, 23, 30, 38, ...

%C 6, 9, 13, 18, 24, 31, 39, 48, ...

%C 10, 14, 19, 25, 32, 40, 49, 59, ...

%C 15, 20, 26, 33, 41, 50, 60, 71, ...

%C 21, 27, 34, 42, 51, 61, 72, 84, ...

%C 28, 35, 43, 52, 62, 73, 85, 98, ...

%F a(n) = A004736(prime(n)). - _Michel Marcus_, Feb 24 2023

%e The 8th prime, 19, is in column 3, so a(8) = 3.

%o (PARI) f(n) = 1 + binomial(1 + floor(1/2 + sqrt(2*n)), 2) - n; \\ A004736

%o a(n) = f(prime(n)); \\ _Michel Marcus_, Feb 24 2023

%Y Cf. A000027, A000040, A004736, A185787.

%Y See A057060 for primes in rows.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jul 30 2000

%E Edited by _Clark Kimberling_, Feb 12 2013