A257639 a(n) is the minimal position at which the maximal value of row n appears in row n of triangle A008289.
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
Offset: 1
Keywords
Examples
For n=9, a(9)=2 because A003056(9)=3 and max{Q(9,p), p=1..3}=4 and Q(9,2)=4.
Links
- Gheorghe Coserea, Table of n, a(n) for n = 1..50000
- Paul Erdős, On some asymptotic formulas in the theory of partitions, Bull. Amer. Math. Soc. 52 (1946), no. 2, 185--188.
- B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae 49 (1995), pp. 86-97.
- G. Szekeres, Some asymptotic formulas in the theory of partitions (II), Quart. J. Math. Oxford (2), 4(1953), 96-111.
Programs
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PARI
Q(N) = { my(q = vector(N)); q[1] = [1, 0, 0, 0]; for (n = 2, N, my(m = (sqrtint(8*n+1) - 1)\2); q[n] = vector((1 + (m>>2)) << 2); q[n][1] = 1; for (k = 2, m, q[n][k] = q[n-k][k] + q[n-k][k-1])); return(q); }; seq(N) = { my(a = vector(N), q = Q(N), vmx = apply(vecmax, q)); for (n = 1, N, a[n] = vecmin(select(v->v==vmx[n], q[n], 1))); a; }; seq(86) \\ updated by Gheorghe Coserea, Jun 02 2018
Comments