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 A212814 a(n) = number of integers k >= 7 such that A212813(k) = n. 7
 1, 3, 11, 2632 (list; graph; refs; listen; history; text; internal format)
 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 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: A124984 A287432 A034797 * A101710 A088799 A181405 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

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)