A105162 The sum of a triangular array made from a negative 6 fold permutation product with shifts up and down of {2,6}.

10, 1, 8, 27, 40, 55, 228, 175, 336, 455, 450, 741, 770, 861, 1274, 1377, 2080, 1595, 2622, 2145, 2840, 3315, 3564, 4275, 5148, 4655, 5454, 5777, 6440, 6327, 9030, 7625, 10564, 9135, 13330, 9425, 14628, 11431, 16224, 13167, 18870, 13825, 20720, 15471

Offset

1,1

Comments

Triangle begins : {10} {-2, 3} {-4, 6, -10} {18, -27, 45, -63} {-10, 15, -25, 35, -55} {-22, 33, -55, 77, -121, 143} The idea was to find permutation function that gave small sums.

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = if 10 Mod[Prime[n], 10] is 1 then -Prime[n]-6 if 3 then -Prime[n]-2 else if 7 then Prime[n]-2, if 9 then Prime[n]-6 a[1]=-5 a[3]=2 T(n, k)=a(k)*Prime[n]*(-1)^k aout[n]=Sum[T(n, k], {k, 1, n]

Mathematica

a[n_] := -(Prime[n] + 6) /; 10 - Mod[Prime[n], 10] == 1; a[n_] := -(Prime[n] + 2) /; 10 - Mod[Prime[n], 10] == 3; a[n_] := Prime[n] - 2 /; (10 - Mod[Prime[n], 10] == 7); a[n_] := Prime[n] - 6 /; (10 - Mod[Prime[n], 10] == 9); a[1] = -Prime[3]; a[3] = Prime[1]; digits = 200 Table[Abs[Apply[Plus, Table[Prime[n]*a[m]*(-1)^n, {n, 1.m}]]], {m, 1, digits}]

Crossrefs

Sequence in context: A092030 A014538 A160928 * A010184 A107830 A144261

Adjacent sequences: A105159 A105160 A105161 * A105163 A105164 A105165

Keyword

nonn,uned

Author

Roger L. Bagula, Apr 10 2005

Status

approved