A375481 Starting numbers for the terms in A035333.

1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 2, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 3, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 4, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 5, 57, 58

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(19) = 12 since A035333(19) = 1213, the concatenation of 12 and 13.
a(20) =  1 since A035333(20) = 1234, the concatenation of 1, 2, 3 and 4.

Mathematica

ConsecutiveNumber[num_, numberOfNumbers_] := Module[{},
  If[numberOfNumbers == 1, Return[num]];
  FromDigits@(IntegerDigits[num]~Join~
     IntegerDigits@ConsecutiveNumber[num + 1, numberOfNumbers - 1])
 ]
ConsecutiveNumberDigits[maxDigits_] := Module[{numList = {}, c, d},
  Do[
   numList =
     numList~Join~(Association[# -> ConsecutiveNumber[#, c]] & /@
        Range[Power[10, d - 1], Power[10, d] - 1]); ,
   {d, 1, Floor[maxDigits/2]}, {c, 2, Floor[maxDigits/d]}
   ];
  SortBy[Select[numList, Values[#][[1]] < Power[10, maxDigits] &],
   Values[#] &]
 ]
Keys[ConsecutiveNumberDigits[8]]//Flatten (* number in this line corresponds to the maximum number of digits of the concatenated terms *)

Prog

(Python)
import heapq
from itertools import islice
def agen(): # generator of terms
    c = 12
    h = [(c, 1, 2)]
    nextcount = 3
    while True:
        (v, s, l) = heapq.heappop(h)
        yield s
        if v >= c:
            c = int(str(c) + str(nextcount))
            heapq.heappush(h, (c, 1, nextcount))
            nextcount += 1
        l += 1; v = int(str(v)[len(str(s)):] + str(l)); s += 1
        heapq.heappush(h, (v, s, l))
print(list(islice(agen(), 70))) # Michael S. Branicky, Aug 18 2024

Crossrefs

For the terms generated by consecutive concatenations see A035333.For concatenations of various numbers of consecutive integers see A000027 (k=1), A127421 (k=2), A001703 (k=3), A279204 (k=4).For primes that are the concatenation of two or more consecutive integers see A052087.

Sequence in context: A053830 A033929 A025482 * A023125 A319657 A255594

Adjacent sequences: A375478 A375479 A375480 * A375482 A375483 A375484

Keyword

easy,nonn,base

Author

Nicholas M. R. Frieler, Aug 17 2024

Status

approved