A377423 -id:A377423 - cp's OEIS frontend

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

M. F. Hasler, Oct 30 2024

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

			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.

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

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

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

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

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

A377474 Indices where new terms arise among first differences of Colombian or self numbers (A377472).

Original entry on oeis.org

1, 5, 103, 984, 9785, 97786, 977787, 9777788, 97777789

Offset: 1

M. F. Hasler, Oct 30 2024

See A377473 for the distinct values of the first differences in the order they appear for the first time.

			The first value, A377472(1) = 2, appears obviously at index a(1) = 1.
The next three values are the same, but at index a(2) = 5 we have a new, distinct value A377472(5) = 11 = A377423(2).
The next distinct value is A377472(103) = 15 = A377423(3), so a(3) = 103.
Then the next new value is A377472(984) = 28 = A377423(4), so a(4) = 984.
The next new value is A377472(9785) = 41 = A377423(5), so a(5) = 9785.
Then, at n = 97786 = a(6), we have A377472(n) = 54 = A377423(6).
Only at n = 977787 = a(7), we have a new value, A377472(n) = 67 = A377423(7).
At n = 9777788 = a(8), we have the next new value, A377472(n) = 80 = A377423(8).

Cf. A003052 (Colombian numbers), A377472 (1st differences of Colombian numbers), A377473 (distinct values of A377472 in order of appearance), A377423 (= A377473 - 1).

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,c); #L

a(n+1) = a(n) + 88*10^(n-1) + 1 for n = 3, 4, ..., 7 at least.

a(9) from Daniel Mondot, May 01 2025

cp's OEIS Frontend

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

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