A035333 Concatenation of two or more consecutive positive integers.

12, 23, 34, 45, 56, 67, 78, 89, 123, 234, 345, 456, 567, 678, 789, 910, 1011, 1112, 1213, 1234, 1314, 1415, 1516, 1617, 1718, 1819, 1920, 2021, 2122, 2223, 2324, 2345, 2425, 2526, 2627, 2728, 2829, 2930, 3031, 3132, 3233, 3334, 3435, 3456, 3536, 3637, 3738

Offset

1,1

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Prog

(Python)
import heapq
from itertools import islice
def agen():
    c = 12
    h = [(c, 1, 2)]
    nextcount = 3
    while True:
        (v, s, l) = heapq.heappop(h)
        yield v
        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(), 47))) # Michael S. Branicky, Dec 23 2021

Crossrefs

For concatenations of exactly k consecutive integers see A000027 (k=1), A127421 (k=2), A001703 (k=3), A279204 (k=4).

See also A007908 for concatenation of 1 through n.

For primes see A052087.

All of A007908, A052087, A053067, A279610 are subsequences.

Sequence in context: A228157 A363820 A072485 * A001704 A127421 A112131

Adjacent sequences: A035330 A035331 A035332 * A035334 A035335 A035336

Keyword

easy,nonn,base

Author

Erich Friedman

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010

Corrected by Paul Tek, Jun 08 2013

Status

approved