A057061 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; ...

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

Offset: 1

Author

Clark Kimberling, Jul 30 2000

Keywords

• nonn

Comments

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

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

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

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

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

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

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

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

Examples

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

Crossrefs

Cf. A000027, A000040, A004736, A185787.

See A057060 for primes in rows.

Programs

PARI

f(n) = 1 + binomial(1 + floor(1/2 + sqrt(2*n)), 2) - n; \\ A004736
a(n) = f(prime(n)); \\ Michel Marcus, Feb 24 2023

Formula

a(n) = A004736(prime(n)). - Michel Marcus, Feb 24 2023

Extensions

Edited by Clark Kimberling, Feb 12 2013