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

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..8.

Formula

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

Example

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).

Prog

(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<N||break); o=n); L}

Crossrefs

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

Sequence in context: A052138 A308459 A142418 * A159523 A172116 A007619

Adjacent sequences: A377471 A377472 A377473 * A377475 A377477 A377478

Keyword

nonn,more

Author

M. F. Hasler, Oct 30 2024

Status

approved