A163128 -id:A163128 - cp's OEIS frontend

A163139 First differences of A163128.

1, 1, 1, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 10

Offset: 1

Juri-Stepan Gerasimov, Jul 21 2009

First differences of self numbers, minus 1.

			a(6) = 24 - 14 = 10.

Cf. A003052, A163128.

A007953 := proc(n) add(d,d=convert(n,base,10)) ; end:
isA003052 := proc(n) for k from 1 to n do if k+A007953(k) = n then RETURN(false) ; fi; od: true; end:
A003052 := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do if isA003052(a) then RETURN(a) ; fi; od: fi; end:
for n from 1 to 100 do printf("%d,",A003052(n+1)-A003052(n)-1) ; od: # R. J. Mathar, Jul 31 2009

a(n) = A163128(n+1) - A163128(n) = A003052(n+1) - A003052(n) - 1.

Missing 10's inserted by R. J. Mathar, Jul 31 2009

A377472 First differences of Colombian or self numbers A003052.

Original entry on oeis.org

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

M. F. Hasler, Oct 29 2024

nonn

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.

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

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

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

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

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

A377423 Distinct values of the number of integers between consecutive self numbers (A163139), in order of occurrence.

Original entry on oeis.org

1, 10, 14, 27, 40, 53, 66, 79, 92, 105, 118, 100, 117, 130, 143, 156, 169, 182, 195, 208, 23, 89, 203, 220, 233, 246, 259, 272, 285, 298, 34, 78, 293, 306, 323, 336, 349, 362, 375, 388, 45, 67, 383, 396, 409, 426, 439, 452, 465, 478, 56, 473, 486, 499

Offset: 1

Daniel Mondot, Oct 27 2024

Each new value is typically found between self numbers located around 10^k, for some k.

This sequences exhibits interesting patterns, for instance, many new numbers are 13 apart.

			Between the first 2 self numbers 1 and 3, there is 1 integer. So 1 is in the sequence
The next new gap is between 9 and 20, with 10 integers, so 10 is in the sequence.
The next new gap is between 1006 and 1021, with 14 integers, so 14 is in the sequence.

Daniel Mondot, Table of n, a(n) for n = 1..10000
Daniel Mondot, First self number found after a new gap value

Cf. A003052, A163128, A163139, A225793, A230093, A230094, A377422, A377472, A377473.

a(n) = A377473(n)-1. - Daniel Mondot, Apr 17 2025

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A163139 First differences of A163128.

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A377472 First differences of Colombian or self numbers A003052.

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A377423 Distinct values of the number of integers between consecutive self numbers (A163139), in order of occurrence.

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