A093915 Triangle with r-th row containing r consecutive integers that sum to the smallest possible proper multiple of A006003(r).

2, 7, 8, 9, 10, 11, 24, 25, 26, 27, 24, 25, 26, 27, 28, 53, 54, 55, 56, 57, 58, 47, 48, 49, 50, 51, 52, 53, 94, 95, 96, 97, 98, 99, 100, 101, 78, 79, 80, 81, 82, 83, 84, 85, 86, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 212, 213, 214, 215, 216, 217

Offset

1,1

Comments

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 proper multiple of A006003(r). There is a simple formula for A093917(r), which allows us to calculate A093915(n) directly. - M. F. Hasler, Apr 04 2009

Links

Table of n, a(n) for n=1..72.

Example

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 proper (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 proper 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.

Prog

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

Crossrefs

Cf. A093916, A093917, A093918.

Sequence in context: A043054 A107225 A253251 * A152769 A283565 A047527

Adjacent sequences: A093912 A093913 A093914 * A093916 A093917 A093918

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 25 2004

Extensions

Edited and extended (values beyond a(15), example, PARI code) by M. F. Hasler, Apr 04 2009

Status

approved