This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212814 #32 Jul 09 2025 04:34:10 %S A212814 1,3,11,2632 %N A212814 a(n) = number of integers k >= 7 such that A212813(k) = n. %C A212814 The next term may be very large, see A212815. %C A212814 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). %D A212814 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) %H A212814 Hans Havermann, <a href="http://chesswanks.com/seq/a212814(4).txt">Conjecture regarding A212814(4)</a> %e A212814 The 11 numbers k for which A212813(k)=2 are 9, 11, 14, 20, 24, 27, 28, 40, 45, 48, 54 (see A212816). %Y A212814 Cf. A036288, A212813, A212815, A212816, A212908, A212909. %K A212814 nonn %O A212814 0,2 %A A212814 _N. J. A. Sloane_, May 30 2012. I added _Hans Havermann_'s comment May 31 2012