A116360 Smallest number having exactly n partitions into products of two successive primes (A006094), or -1 if no such number exists.

1, 6, 30, 60, 90, 105, 120, 135, 143, 158, 155, 167, 173, 182, 185, 207, 197, 203, 212, 215, 221, 231, 227, 233, 239, 242, 256, 245, 251, 261, 257, 260, 263, 266, 282, 272, 275, 278, 281, 291, -1, 287, 290, 293, 296, 309, 312, 302, 305, 319, 308, 314, -1, 317, 322, 320

Offset

0,2

Comments

If a(n) <> -1: A116357(a(n))=n and A116357(m)<>n for m<n.

From David A. Corneth, Sep 11 2024: (Start)

To prove a value -1 we need two facts:

1. For some k we have A116357(k), A116357(k+1), A116357(k+2), A116357(k+3), A116357(k+4), A116357(k+5) > n as A116357(k + 6) >= A116357(k) for all k.

2. A116357(m) != n for 1 <= m < k. (End)

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

Example

Without proof: a(40) = -1 and a(52) = -1.
a(40) = -1 as A116357(296) through A116357(296+5) are larger than 40 and for 1 <= m < 296 we have A116357(m) != 40. - David A. Corneth, Sep 11 2024

Crossrefs

Cf. A006094, A116357.

Sequence in context: A024365 A057229 A120734 * A336219 A065800 A181827

Adjacent sequences: A116357 A116358 A116359 * A116361 A116362 A116363

Keyword

sign

Author

Reinhard Zumkeller, Feb 12 2006

Extensions

Edited by D. S. McNeil, Sep 06 2010

Status

approved