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

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

Offset: 1

Author

M. F. Hasler, Oct 30 2024

Keywords

• nonn
• more

Comments

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

Examples

			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).
		

Crossrefs

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

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,c); #L
				

Formula

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

Extensions

a(9) from Daniel Mondot, May 01 2025