A279610 -id:A279610 - cp's OEIS frontend

A053067 a(n) is the concatenation of next n numbers (omit leading 0's).

1, 23, 456, 78910, 1112131415, 161718192021, 22232425262728, 2930313233343536, 373839404142434445, 46474849505152535455, 5657585960616263646566, 676869707172737475767778, 79808182838485868788899091, 9293949596979899100101102103104105, 106107108109110111112113114115116117118119120

Offset: 1

Felice Russo, Feb 25 2000

Concatenation of the integers from A000124(n-1) up to and including A000217(n). - R. J. Mathar, Aug 30 2013

The second term is a prime. When is the next prime, if there is another? - N. J. A. Sloane, Dec 16 2016

Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000.

Michael S. Branicky, Table of n, a(n) for n = 1..200

A subsequence of A035333. For primes in latter, see A052087.

See A279610 for a variant.

Table[FromDigits[Flatten[IntegerDigits/@Range[(n(n-1))/2+1,(n(n+1))/2]]],{n,20}] (* Harvey P. Dale, Jan 23 2016 *)

a(n) = my(s = ""); for (i=n*(n-1)/2 + 1, n*(n+1)/2, s = concat(s, Str(i));); eval(s); \\ Michel Marcus, Aug 11 2017

def a(n): return int("".join(map(str, range((n-1)*n//2+1, n*(n+1)//2+1))))
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Jan 23 2021

More terms from James Sellers, Feb 28 2000

More terms from Michel Marcus, Aug 11 2017

A035333 Concatenation of two or more consecutive positive integers.

Original entry on oeis.org

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

Erich Friedman

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

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.

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

Edited by Charles R Greathouse IV, Apr 28 2010

Corrected by Paul Tek, Jun 08 2013

cp's OEIS Frontend

A053067 a(n) is the concatenation of next n numbers (omit leading 0's).

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