A125769 a(n) is the least number j such that j*T_k +/- 1 is n-th prime for some k-th triangular number.

1, 2, 1, 1, 1, 2, 3, 2, 4, 1, 2, 1, 2, 2, 8, 9, 4, 4, 1, 2, 2, 1, 3, 2, 16, 10, 17, 3, 2, 4, 6, 2, 1, 5, 10, 10, 2, 27, 6, 29, 4, 2, 1, 32, 3, 3, 1, 8, 38, 23, 3, 2, 2, 7, 43, 4, 6, 2, 1, 10, 47, 14, 2, 4, 4, 53, 5, 12, 58, 35, 59, 3, 61, 62, 1, 64, 5, 6, 40, 3, 2, 2, 12, 12, 8, 74, 10, 76, 2, 2, 6, 4

Offset

1,2

Comments

Eventually all primes p appear since (p +/-1) times 1(1+1)/2 equals (p +/- 1).

If we asked for the least number k then k always equals 1 since all primes p appear since (p +/-1) times 1(1+1)/2 equals (p +/- 1).

The k's for the corresponding j's are: round(sqrt(2p/j)).

First occurrence of i is A125770: 1, 2, 7, 9, 34, 31, 54, 15, 16, 26, 148, 68, 398, 62, 193, 25, 27, 140, 550, 397, 107, 113, ...,.

Links

Table of n, a(n) for n=1..92.

Example

a(1) = 1 because 1*1+1 = 2 which is the first prime,
a(2) = 2 because 2*1+1 = 3 which is the second prime,
a(3) = 4 because 1*6-1 = 5 which is the third prime,
a(8) = 3 because 2*10-1 = 19 which is the eighth prime, ...

Mathematica

triQ[n_] := IntegerQ@ Sqrt[8n + 1]; f[n_] := Block[{j = 1, p = Prime@n}, While[ !triQ[(p - 1)/j] && !triQ[(p + 1)/j], j++ ]; j]; Array[f, 92]

Crossrefs

Cf. A000217, A125765, A125766, A125767, A125768, A125770.

Sequence in context: A029344 A316854 A367759 * A367799 A272084 A003023

Adjacent sequences: A125766 A125767 A125768 * A125770 A125771 A125772

Keyword

nonn

Author

Jonathan Vos Post & Robert G. Wilson v, Dec 01 2006

Status

approved