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

Author

Reinhard Zumkeller, Feb 12 2006

Keywords

• sign

Comments

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

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)

Examples

			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
		

Links

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

Crossrefs

Cf. A006094, A116357.

Extensions

Edited by D. S. McNeil, Sep 06 2010

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