1,1

The r-th row constructed as explained in the example starts with x=A093916(r), ends with x+r-1=A093918(r), and has its sum A093917(r) equal to the smallest strict multiple of A006003(r). There is a simple formula for A093917(r), which allows us to calculate A093915(n) directly. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 04 2009

Given the triangle

1 . . . . with row sum S1 = 1 = A006003(1)

2,3 . . . with row sum S2 = 2+3 = 5 = A006003(2)

4,5,6 . . with row sum S3 = 4+5+6 = 15 = A006003(3), etc.,

the sequence is constructed as follows:

The first row below must be a strict (i.e. > 1) multiple of S1; the smallest possibility is [ 2 ].

The next row below must contain 2 consecutive integers with sum equal to a strict multiple of S2=5. It cannot be 10 (not the sum of 2 consecutive integers), but 15 = 7+8 is a possibility.

The third row [x,x+1,x+2] must sum to a multiple of S3=15, and 2*S3=30 is possible for x=9.

The 4th row [x,x+1,x+2,x+3] must have its sum 4x+6 equal to a multiple of S4=7+8+9+10=34, and x=24 gives the sum 102=3*34, while 2*34=68 can't be achieved for any integer x.

This gives:

2 . . . . . . . with row sum 2 = 2*S1

7,8 . . . . . . with row sum 7+8 = 15 = 3*S2

9,10,11 . . . . with row sum 9+10+11 = 30 = 2*S3

24,25,26,27 . . with row sum 24+25+26+27 = 102 = 3*S4.

(PARI) for(r=1, 9, x=A093916(r)-1; for(c=1, r, print1(x+c, ", "))) /* M. F. Hasler, Apr 04 2009 */

Cf. A093916, A093917, A093918.

Sequence in context: A152778 A043054 A107225 this_sequence A152769 A047527 A064517

Adjacent sequences: A093912 A093913 A093914 this_sequence A093916 A093917 A093918

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 25 2004

Edited and extended (values beyond a(15), example, PARI code) by M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 04 2009