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A093915 Triangle with r-th row containing r consecutive integers that sum to the smallest possible proper multiple of A006003(r). 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)