A212814 - OEIS

A212814

a(n) = number of integers k >= 7 such that A212813(k) = n.

1, 3, 11, 2632

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OFFSET

0,2

COMMENTS

The next term may be very large, see A212815.

Comment from Hans Havermann, Sequence Fans Mailing List, May 31 2012: The 11 numbers k for which A212813(k)=2 are 9, 11, 14, 20, 24, 27, 28, 40, 45, 48, 54. Empirically, it appears that 2632 is the sum of the number of prime partitions (A000607) of the eleven numbers 8, 10, 13, 19, 23, 26, 27, 39, 44, 47, 53. I hesitate turning this into a conjecture only because the 3 numbers k for which A212813(k)=1 are 7, 10, 12 and the sum of the number of prime partitions of the three numbers 6, 9, 11 is twelve, not eleven (the extra partition being, I think, 2+2+2).

REFERENCES

Bellamy, O. S.; Cadogan, C. C. Subsets of positive integers: their cardinality and maximality properties. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 167--178, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561043 (82b:10006)

LINKS

Table of n, a(n) for n=0..3.

Hans Havermann, Conjecture regarding A212814(4)

EXAMPLE

The 11 numbers k for which A212813(k)=2 are 9, 11, 14, 20, 24, 27, 28, 40, 45, 48, 54 (see A212816).

CROSSREFS

Cf. A036288, A212813, A212815, A212816, A212908, A212909.

Sequence in context: A287432 A353085 A034797 * A101710 A088799 A372101

Adjacent sequences: A212811 A212812 A212813 * A212815 A212816 A212817

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 30 2012. I added Hans Havermann's comment May 31 2012.

STATUS

approved