A057060 a(n) = number of the row of (R(i,j)) that contains prime(n), where R(i,j) is the rectangle with descending antidiagonals 1; 2,3; 4,5,6; ...

1, 2, 2, 1, 1, 3, 2, 4, 2, 1, 3, 1, 5, 7, 2, 8, 4, 6, 1, 5, 7, 1, 5, 11, 6, 10, 12, 2, 4, 8, 7, 11, 1, 3, 13, 15, 4, 10, 14, 2, 8, 10, 1, 3, 7, 9, 1, 13, 17, 19, 2, 8, 10, 20, 4, 10, 16, 18, 1, 5, 7, 17, 7, 11, 13, 17, 6, 12, 22, 24, 2, 8, 16, 22, 1, 5, 11

Offset: 1

Author

Clark Kimberling, Jul 30 2000

Keywords

• nonn

Comments

The rectangle 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 row 4, so a(8) = 4.
		

Crossrefs

Cf. A000027, A000040, A002260, A185787.

See A057061 for primes in columns.

Programs

Mathematica

s = Flatten[Table[Range[n], {n, 1, 40}]];
Table[s[[Prime[n]]], {n, 1, 100}]

PARI

f(n) = n-binomial((sqrtint(8*n)+1)\2, 2); \\ A002260
a(n) = f(prime(n)); \\ Michel Marcus, Feb 24 2023

Formula

a(n) = A002260(prime(n)). - Kevin Ryde, Feb 12 2023

Extensions

Edited by Clark Kimberling, Feb 13 2023