A377472 First differences of Colombian or self numbers A003052.

2, 2, 2, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 15, 11

Offset: 1

Author

M. F. Hasler, Oct 29 2024

Keywords

• nonn

Comments

Most terms are equal to 11.

Up to a(103) = 15, the only exceptions are a(n) = 2 for n = 1, 2, 3, 4, 14, 24, ..., 94.

Then a(n) = 2 for n = 112, 122, ..., 192, and a(201) = 15.

Then a(n) = 2 for n = 210, 220, ..., 290, and a(299) = 15.

This pattern repeats 8 times, with a(n) = 15 for n = 397, 495, ..., 887.

Then a(984) = 28, after which the previous pattern resumes, with a(n) = 2 for n = 992, 1002, ..., 1072, then a(n) = 15 for n = 1081, 1179, ..., 1865.

This larger pattern continues with a(n) = 28 for n = 1962, 2940, 3918, ..., 8808.

A still larger pattern starts at a(9785) = 41, after which the previous pattern repeats with a(9881) = 15, later a(10762) = 28 etc.

Links

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

Crossrefs

Cf. A003052 (Colombian or self numbers), A377473 (range of this sequence), A377474 (indices where new terms appear), A163128, A163139.

Programs

PARI

A377472_upto(N=99)={my(o,L=List()); for(n=1+o=1,oo,if(is_A003052(n), listput(L,n-o); o=n; #L
				

Formula

a(n) = A003052(n+1) - A003052(n).

a(n) = A163139(n) + 1 = A163128(n+1) - A163128(n) + 1. - Max Alekseyev, Jan 02 2025