A279204 -id:A279204 - cp's OEIS frontend

A001703 Decimal concatenation of n, n+1, and n+2.

12, 123, 234, 345, 456, 567, 678, 789, 8910, 91011, 101112, 111213, 121314, 131415, 141516, 151617, 161718, 171819, 181920, 192021, 202122, 212223, 222324, 232425, 242526, 252627, 262728, 272829, 282930, 293031, 303132, 313233, 323334, 333435, 343536, 353637, 363738

Offset: 0

mag(AT)laurel.salles.entpe.fr

All terms are divisible by 3. Every third term starting with a(2) is divisible by 9. - Alonso del Arte, May 27 2013

			a(8) = 8910 since the three consecutive numbers starting with 8 are 8, 9, 10, and these concatenate to 8910. (This is the first term that differs from A193431).

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A074991.
For concatenations of exactly k consecutive integers see A000027 (k=1), A127421 (k=2), A279204 (k=4). For 2 or more see A035333.
See also A127422, A127423, A127424.

read(transforms) :
A001703 := proc(n)
    digcatL([n,n+1,n+2]) ;
end proc:
seq(A001703(n),n=1..20) ; # R. J. Mathar, Mar 29 2017
# Third Maple program:
a:= n-> parse(cat(n, n+1, n+2)):
seq(a(n), n=0..50); # Alois P. Heinz, Mar 29 2017

concat3Nums[n_] := FromDigits@ Flatten@ IntegerDigits[{n, n + 1, n + 2}]; Array[concat3Nums, 25] (* Robert G. Wilson v *)

a(n)=eval(Str(n,n+1,n+2)) \\ Charles R Greathouse IV, Oct 08 2011

for n in range(100): print(int(str(n)+str(n+1)+str(n+2))) # David F. Marrs, Sep 18 2018

The portion of the sequence with all three numbers having d digits - i.e., n in 10^(d-1)..10^d-3 - is in arithmetic sequence: a(n) = (10^(2*d)+10^d+1)*n + (10^d+2). - Franklin T. Adams-Watters, Oct 07 2011

Initial term 12 added and offset changed to 0 at the suggestion of R. J. Mathar. - N. J. A. Sloane, Mar 29 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

A127421 Numbers whose decimal expansion is a concatenation of 2 consecutive increasing nonnegative numbers.

Original entry on oeis.org

1, 12, 23, 34, 45, 56, 67, 78, 89, 910, 1011, 1112, 1213, 1314, 1415, 1516, 1617, 1718, 1819, 1920, 2021, 2122, 2223, 2324, 2425, 2526, 2627, 2728, 2829, 2930, 3031, 3132, 3233, 3334, 3435, 3536, 3637, 3738, 3839, 3940, 4041, 4142, 4243, 4344, 4445, 4546

Offset: 1

Artur Jasinski, Jan 14 2007

Primes in the sequence are in A030458. - Bruno Berselli, Mar 25 2015

a(n) always has an even number of digits unless n is in A103456. - Alonso del Arte, Oct 30 2019

			a(1) = "0,1" = 1.
a(13) = "12,13" = 1213.

N. J. A. Sloane, Table of n, a(n) for n = 1..25000

A variant of A001704.
For concatenations of exactly k consecutive integers see A000027 (k = 1), A127421 (k = 2), A001703 (k = 3), A279204 (k = 4). For 2 or more see A035333.
Cf. A030458, A127423, A127424, A127425, A103456.

[Seqint(Intseq(n+1) cat Intseq(n)): n in [0..50]]; // Bruno Berselli, Mar 25 2015

a:= n-> parse(cat(n-1, n)):
seq(a(n), n=1..55);  # Alois P. Heinz, Jul 05 2018

nMax = 49; digitsList = IntegerDigits[Range[0, nMax]]; Table[FromDigits[Flatten[{digitsList[[n]], digitsList[[n + 1]]}]], {n, nMax - 1}] (* Alonso del Arte, Oct 24 2019 *)
Table[FromDigits[Flatten[IntegerDigits/@{n,n+1}]],{n,0,50}] (* Harvey P. Dale, May 16 2020 *)

for n in range(100): print(int(str(n)+str(n+1))) # David F. Marrs, Sep 17 2018

val numerStrs = (0 to 49).map(Integer.toString(_)).toList
val concats = (numerStrs.dropRight(1)) zip (numerStrs.drop(1))
concats.map(x => Integer.parseInt(x.1 + x._2)) // _Alonso del Arte, Oct 24 2019

More terms from Joshua Zucker, May 15 2007

A030471 Primes which are concatenations of four consecutive numbers.

Original entry on oeis.org

4567, 14151617, 20212223, 34353637, 58596061, 64656667, 118119120121, 140141142143, 148149150151, 176177178179, 196197198199, 218219220221, 220221222223, 236237238239, 238239240241, 268269270271, 278279280281

Offset: 1

Patrick De Geest

There are no primes which are concatenations of three consecutive numbers (A001703), in fact all such concatenations are divisible by 3. - Zak Seidov, Oct 25 2014

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Cf. A001703, A030470, A084551.

A279204[n_] := FromDigits[Flatten[IntegerDigits[Range[n, n + 3]]]];
Select[Array[A279204, 500], PrimeQ] (* Paolo Xausa, Aug 26 2024 *)

lista(nn) = for(n=1, nn, if (isprime(q=eval(concat(concat(concat(Str(n), Str(n+1)), Str(n+2)), Str(n+3)))), print1(q, ", "))); \\ Michel Marcus, Oct 26 2014

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    strs = ["1", "2", "3", "4"]
    for k in count(1):
        if isprime(t:=int("".join(strs))): yield t
        strs = strs[1:] + [str(k+4)]
print(list(islice(agen(), 20))) # Michael S. Branicky, Aug 26 2024

Edited by Charles R Greathouse IV, Apr 23 2010

A287747 Concatenation {n, n + 1,.., n + 9}.

Original entry on oeis.org

12345678910, 234567891011, 3456789101112, 45678910111213, 567891011121314, 6789101112131415, 78910111213141516, 891011121314151617, 9101112131415161718, 10111213141516171819, 11121314151617181920, 12131415161718192021, 13141516171819202122, 14151617181920212223

Offset: 1

XU Pingya, Jun 01 2017

For the position of primes in this sequence, see A287244.

Paolo Xausa, Table of n, a(n) for n = 1..1000

Cf. A001704, A001703, A279204, A287244.

A287747[n_] := FromDigits[Flatten[IntegerDigits[Range[n, n + 9]]]];
Array[A287747, 25] (* Paolo Xausa, Aug 26 2024 *)

A375481 Starting numbers for the terms in A035333.

Original entry on oeis.org

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

Nicholas M. R. Frieler, Aug 17 2024

			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.

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

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.

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 *)

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

A375692 Decimal concatenation of the 5 numbers n,n+1,n+2,n+3,n+4.

Original entry on oeis.org

12345, 23456, 34567, 45678, 56789, 678910, 7891011, 89101112, 910111213, 1011121314, 1112131415, 1213141516, 1314151617, 1415161718, 1516171819, 1617181920, 1718192021, 1819202122, 1920212223, 2021222324, 2122232425, 2223242526, 2324252627, 2425262728, 2526272829

Offset: 1

Viljo Huhtala, Aug 25 2024

Cf. A001703, A001704, A193493, A279204.

Table[FromDigits[Join[Flatten[IntegerDigits/@{n,n+1,n+2,n+3,n+4}]]],{n,25}] (* James C. McMahon, Oct 11 2024 *)

a(n) = eval(concat(vector(5, i, Str(n+i-1)))); \\ Michel Marcus, Sep 17 2024

def a(n): return int(str(n)+str(n+1)+str(n+2)+str(n+3)+str(n+4))

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A001703 Decimal concatenation of n, n+1, and n+2.

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A035333 Concatenation of two or more consecutive positive integers.

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A127421 Numbers whose decimal expansion is a concatenation of 2 consecutive increasing nonnegative numbers.

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A030471 Primes which are concatenations of four consecutive numbers.

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A287747 Concatenation {n, n + 1,.., n + 9}.

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A375481 Starting numbers for the terms in A035333.

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A375692 Decimal concatenation of the 5 numbers n,n+1,n+2,n+3,n+4.

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Mathematica

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Python