A249723 - OEIS

A249723

Numbers n such that there is a multiple of 9 on row n of Pascal's triangle with property that all multiples of 4 on the same row (if they exist) are larger than it.

9, 10, 13, 15, 18, 19, 21, 27, 29, 31, 37, 39, 43, 45, 46, 47, 54, 55, 59, 63, 75, 79, 81, 82, 83, 85, 87, 90, 91, 93, 95, 99, 103, 109, 111, 117, 118, 119, 123, 126, 127, 135, 139, 151, 153, 154, 157, 159, 162, 163, 165, 167, 171, 175, 181, 183, 187, 189, 190, 191, 198, 199, 207, 219, 223, 225, 226, 229, 231, 234, 235, 237, 239, 243, 245, 247, 251, 253, 255

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All n such that on row n of A095143 (Pascal's triangle reduced modulo 9) there is at least one zero and the distance from the edge to the nearest zero is shorter than the distance from the edge to the nearest zero on row n of A034931 (Pascal's triangle reduced modulo 4), the latter distance taken to be infinite if there are no zeros on that row in the latter triangle.

A052955 from its eight term onward, 31, 47, 63, 95, 127, ... seems to be a subsequence. See also the comments at A249441.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

Row 13 of Pascal's triangle (A007318) is: {1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1} and the term binomial(13, 5) = 1287 = 9*11*13 occurs before any term which is a multiple of 4. Note that one such term occurs right next to it, as binomial(13, 6) = 1716 = 4*3*11*13, but 1287 < 1716, thus 13 is included.

PROG

(PARI)

A249723list(upto_n) = { my(i=0, n=0); while(i<upto_n, for(k=0, n\2, if(!(binomial(n, k)%4), break, if(!(binomial(n, k)%9), i++; write("b249723.txt", i, " ", n); break))); n++); }

CROSSREFS

Complement: A249724.

Natural numbers (A000027) is a disjoint union of the sequences A048278, A249722, A249723 and A249726.

Cf. A007318, A034931, A048645, A051382, A095143, A052955, A249441, A249695.

Cf. A048278, A249722, A249726, A249731, A249732, A249733.

Sequence in context: A178679 A154766 A116594 * A050593 A189834 A248350

Adjacent sequences: A249720 A249721 A249722 * A249724 A249725 A249726

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 04 2014

STATUS

approved