A336109 First column of dispersion array A120861.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 95, 96

Offset: 1

Author

Petros Hadjicostas, Jul 08 2020

Keywords

• nonn

Comments

For n = 1 to 34, we have a(n) = A039216(n), but a(35) = 42 <> = 41 = A039216(35).

Is this the same as A188040? - R. J. Mathar, Jul 22 2020

Indeed, it seems that A336109(1) = A188040(1) and A336109(n) = A188040(n-1) for n >= 3, but A336109(2) = 2 does not appear in A188040. Because of the way A120861 is constructed (cf. Michel Marcus's PARI program below), a(2) = 2 cannot be omitted. - Petros Hadjicostas, Jul 22 2020

Links

• Clark Kimberling, The equation (j+k+1)^2 - 4*k = Q*n^2 and related dispersions, Journal of Integer Sequences, 10 (2007), Article #07.2.7; see Section 5.

Crossrefs

Cf. A039216, A120861, A188040.

Programs

PARI

/* This is Michel Marcus's program from A120861. */
f(n) = 3*n + 2*sqrtint(2*n^2) + 2;
unused(listus) = {my(v=vecsort(Vec(listus))); for (i=1, vecmax(v), if (!vecsearch(v, i), return (i)); ); };
D(nb) = {my(m = matrix(nb, nb), t); my(listus = List); for (g=1, nb, if (g==1, t = 1, t = unused(listus)); m[g, 1]=t; listput(listus, t); t = f(t); m[g, 2]=t; listput(listus, t); for (h=3, nb, t = 6*m[g, h-1] - m[g, h-2]; m[g, h] = t; listput(listus, t); ); ); m; };
firstcol(nb) = my(m=D(nb)); vector(nb, k, m[k, 1]);