A377473 Distinct first differences of Colombian or self numbers (A377472), listed in the order they appear.

2, 11, 15, 28, 41, 54, 67, 80, 93, 106, 119, 101, 118, 131, 144, 157, 170, 183, 196, 209, 24, 90, 204, 221, 234, 247, 260, 273, 286, 299, 35, 79, 294, 307, 324, 337, 350, 363, 376, 389, 46, 68, 384, 397, 410, 427, 440, 453, 466, 479, 57, 474, 487, 500

Offset: 1

Author

M. F. Hasler, Oct 30 2024

Keywords

• nonn
• base

Comments

See A377474 for the indices where these first differences appear for the first time.

Examples

			A377472(n) = 2 = a(1) for all n <= 4. Then, A377472(n) = 11 = a(2) up to n = 13.
Then again, A377472(14..23) = (2, 11, ..., 11) and similarly up to n = 94.
But A377472(103) = 15 = a(3). Then the previous pattern repeats, with A377472(n) = 2 for n = 112, 122, ..., 192, followed by A377472(n) = 15 at n = 201, 299, 397, ..., 887.
Then A377472(984) = 28 = a(4), and it goes on with A377472(n) = 2 at n = 992, 1002, ..., 1072, and so on, with A377472(n) = 28 at n = 1962, 2940, 3918, ..., 8808.
Then A377472(9785) = 41 = a(5), and the whole previous pattern repeats, with A377472(9881) = 15, then A377472(10762) = 28 etc.
At n = 97786, we find A377472(n) = 54 = a(6), and again the whole previous pattern repeats again 8 more times, each time separated by a 54, until we have, at n = 977787, A377472(n) = 67 = a(7). And so on.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003052 (Colombian numbers), A377472 (1st differences of Colombian numbers), A163139 (= A377472 - 1), A377423.

Programs

PARI

A377473_upto(N=9, show=1)={my(o, c, d, L=List()); for(n=1+o=1, oo, is_A003052(n)||next; c++; if(!setsearch(L, d=n-o), show && printf("%d, ",[c,d]); listput(L,d); #L
				

Formula

a(n) = A377423(n) + 1.

Extensions

Terms a(9) onward computed from A377423 by Max Alekseyev, Dec 31 2024