A300062 -id:A300062 - cp's OEIS frontend

A162555 a(n) = the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.

1, 11, 18, 4, 16, 6, 14, 8, 12, 10, 13, 7, 15, 5, 17, 3, 19, 2, 9, 30, 101, 201, 301, 401, 26, 76, 501, 453, 49, 601, 170, 32, 168, 34, 20, 82, 264, 38, 162, 40, 160, 42, 158, 44, 106, 96, 154, 48, 152, 50, 150, 52, 148, 54, 146, 56, 21, 81, 242, 60, 140, 62, 138, 64, 136

Offset: 1

Kerry Mitchell, Jul 06 2009

A permutation of the positive integers. - M. F. Hasler, Mar 05 2018

			a(3) = 18 because that makes the sum of the first 3 terms 30, containing a substring of "3." 11 would make a sum of 23, but 11 was already used in a(2).

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 3000 terms from Jean-Marc Falcoz)
Index entries for sequences that are permutations of the natural numbers

Cf. A160855 for the same concept using strings of binary for the sum and substring.

See A300062 for a strictly increasing variant.

A162555_list, A162555_set, s = [], set(), 0
for i in range(1,10001):
    j, si = 1, str(i)
    while si not in str(s+j) or j in A162555_set:
        j += 1
    A162555_list.append(j)
    A162555_set.add(j)
    s += j # Chai Wah Wu, Feb 23 2018

A300082 a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring.

Original entry on oeis.org

1, 3, 7, 8, 10, 15, 16, 20, 21, 37, 38, 40, 53, 65, 80, 82, 84, 96, 111, 129, 150, 172, 193, 201, 202, 203, 227, 228, 254, 258, 259, 289, 296, 316, 317, 327, 349, 371, 399, 425, 426, 432, 449, 453, 509, 513, 526, 548, 593, 594, 611, 642, 643, 644, 648, 649

Offset: 1

Rémy Sigrist and Chai Wah Wu, Feb 24 2018

This sequence is a binary variant of A300062.

The scatterplot of the first difference has interesting features (see Links section).

			The first terms, alongside the binary representation of Sum_{k=1..n} a(k) with the binary representation of n in brackets, are:
  n     a(n)      bin(Sum_{k=1..n} a(k))
  --    ----      ----------------------
   1       1              (1)
   2       3            (10)0
   3       7           10(11)
   4       8          (100)11
   5      10          11(101)
   6      15         10(110)0
   7      16         (111)100
   8      20        10(1000)0
   9      21        1(1001)01
  10      37       1000(1010)
  11      38       (1011)0000
  12      40       110(1100)0
  13      53      10000(1101)
  14      65      10100(1110)
  15      80      1100(1111)0
  16      82      1111(10000)

Rémy Sigrist, Perl program for A300082
Rémy Sigrist, Scatterplot of the first difference of the first 2^17 terms

Cf. A160855, A300062.

Perl
```
See Links section.
```

cp's OEIS Frontend

A162555 a(n) = the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.

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