A144176 a(n) = abs(b(2n-1) - b(2n)) where b(3n+1) = floor(n/9) + 2, b(3n+2) = (n mod 9) + 2, b(3n+3) = b(3n+1)*b(3n+2) for n >= 0.

0, 2, 3, 2, 6, 5, 4, 10, 7, 6, 14, 9, 8, 17, 4, 0, 6, 8, 2, 12, 12, 4, 18, 16, 6, 24, 20, 2, 4, 9, 0, 12, 15, 2, 20, 21, 4, 28, 27, 6, 35, 8, 2, 10, 16, 0, 20, 24, 2, 30, 32, 4, 40, 40, 4, 6, 15, 2, 18, 25, 0, 30, 35, 2, 42, 45, 4, 53, 12, 4, 14, 24, 2, 28, 36, 0, 42, 48, 2, 56, 60, 6, 8, 21, 4

Offset

1,2

Comments

Old name was: (2*2=4, 2*3=6, 2*4=8, 2*5=10, 2*6=12, 2*7=14, 2*8=16, 2*9=18, 2*10=20, 3*2=6, ...) becomes (abs(2-2, 4-2, 3-6, 2-4, 8-2, 5-10, 2-6, 12-2, 7-14, 2-8, 16-2, 9-18, 2-10, 20-3, 2-6, ...)).

(..., 9*9=81, 9*10=90, 10*2=20, 10*3=30, 10*4=40, 10*5=50, 10*6=60, 10*7=70, 10*8=80, 10*9=90, 10*10=100, 11*2=22, ...) becomes

(abs(..., 9-9, 81-9, 10-90, 10-2, 20-10, 3-30, 10-4, 40-10, 5-50, 10-6, 60-10, 7-70, 10-8, 80-10, 9-90, 10-10, 100-11, 2-22, ...)).

The sequence is generated from a list of triples (i,j,i*j) where i=2,3, ... and j=2,3,...,10. - R. J. Mathar, Apr 29 2010

Links

Table of n, a(n) for n=1..85.

Example

Abs(9-9) = abs(0) = 0 = a(106),
Abs(81-9) = abs(72) = 72 = a(107),
Abs(10-90) = abs(-80) = 80 = a(108),
Abs(10-2) = abs(8) = 8 = a(109),
Abs(20-10) = abs(10) = 10 = a(110),
Abs(3-30) = abs(-27) = 27 = a(111), etc.

Maple

pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [] ; for i from 2 to nmax do for j from 2 to 10 do n := i*j ; a := [op(a), i, j, n] ; od: od: a ; end: L := pflat2(30) ; for n from 1 to nops(L)-2 by 2 do printf("%d, ", abs(op(n, L)-op(n+1, L)) ) ; end do: # R. J. Mathar, Apr 29 2010

Mathematica

Abs[Subtract @@@ Partition[Flatten@ Table[{n, k, n k}, {n, 2, 10}, {k, 2, 10}], 2, 2]] (* Michael De Vlieger, Oct 24 2022 *)

Prog

(PARI) a(n) = my(k=ceil(n/27), r=n-27*(k-1), v=[]); for(i=2, 10, v=concat(v, [2*k, i, 2*k*i])); for(i=2, 10, v=concat(v, [2*k+1, i, (2*k+1)*i])); abs(v[2*r-1] - v[2*r]) \\ Jianing Song, Oct 24 2022

Crossrefs

Cf. A144177, A144178.

Sequence in context: A286587 A054126 A323507 * A307686 A077418 A005421

Adjacent sequences: A144173 A144174 A144175 * A144177 A144178 A144179

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Nov 19 2008

Extensions

Entries checked by R. J. Mathar, Apr 29 2010

New name from Jianing Song, Nov 01 2022

Status

approved