A215027 -id:A215027 - cp's OEIS frontend

A001704 a(n) = n concatenated with n + 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

N. J. A. Sloane

See A030457 for the indices of prime terms in this sequence. - Reinhard Zumkeller, Jun 27 2015 [Simplified by Jianing Song, Jan 27 2019]

N. J. A. Sloane, Table of n, a(n) for n = 1..25000 (first 1000 terms from T. D. Noe)

See A127421 for a version with offset 0.

Cf. A215027, A248378, A030457.

a001704 n = a001704_list !! (n-1)
a001704_list = map read (zipWith (++) iss $ tail iss) :: [Integer]
               where iss = map show [1..]
-- Reinhard Zumkeller, Oct 07 2014

[Seqint(Intseq(n+1) cat Intseq(n)): n in [1..50]]; // Vincenzo Librandi, Jul 08 2018

f:=proc(i) i*10^(1+floor(evalf(log10(i+1), 10)))+i+1; end: # gives a(n) - N. J. A. Sloane, Aug 04 2012
# alternative Maple program:
a:= n-> parse(cat(n, n+1)):
seq(a(n), n=1..55);  # Alois P. Heinz, Jul 05 2018

Table[FromDigits@Flatten@IntegerDigits[{n, n + 1}], {n, 100}] (* T. D. Noe, Aug 09 2012 *)

a(n)=eval(Str(n,n+1)) \\ Charles R Greathouse IV, Jul 23 2016
(Emacs Lisp)
;; Concatenation
(defun A001704 (n) (string-to-int (concat (int-to-string n) (int-to-string (1+ n)))))
;; Formula
(defun A001704 (n) (1+ n (* n (expt 10 (1+ (floor (log (1+ n) 10)))))))
(mapcar '(lambda (n) (cons n (A001704 n))) '(1 2 3 10 11 12 99 999)) => ((1 . 12) (2 . 23) (3 . 34) (10 . 1011) (11 . 1112) (12 . 1213) (99 . 99100) (999 . 9991000))
; Tim Chambers, Jul 07 2018

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

val numerStrs = (1 to 50).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 and Jon E. Schoenfield, May 15 2007

A215028 a(1) = 1; for n >= 1, a(n+1) = (concatenation of n+1 and n) - a(n).

Original entry on oeis.org

1, 20, 12, 31, 23, 42, 34, 53, 45, 64, 1046, 165, 1147, 266, 1248, 367, 1349, 468, 1450, 569, 1551, 670, 1652, 771, 1753, 872, 1854, 973, 1955, 1074, 2056, 1175, 2157, 1276, 2258, 1377, 2359, 1478, 2460, 1579, 2561, 1680, 2662, 1781, 2763, 1882, 2864, 1983

Offset: 1

N. J. A. Sloane, Aug 04 2012

A variation of A215027.

Cf. A215027, A127423.

f:=proc(i) (i+1)*10^(1+floor(evalf(log10(i))))+i; end: # A127423
a:=proc(n) option remember; global f; if n=1 then 1 else f(n-1)-a(n-1); fi; end;

A215028(n, print_all=0)={my(a=1); for(n=1, n-1, print_all & print1(a","); a=(n+1)*10^#Str(n)+n-a); a} \\ M. F. Hasler, Aug 23 2012

A371144 The smallest number such that the concatenation of n, a(n), n+1 is divisible by the concatenation of n and n+1.

Original entry on oeis.org

3, 5, 7, 0, 37, 76, 48, 98, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 560, 571, 582, 593, 604, 615, 626, 637, 648, 361, 670, 681, 692, 703, 714, 725, 736, 747, 758, 769, 780

Offset: 1

Scott R. Shannon, Mar 12 2024

For n > 10, when n starts with the digits 1, 2, 3, or 4, then a(n) = 2*n + 1. When n starts with the digits 5, 6, 7, or 8, then a(n) = 11*n + 10 for the vast majority of terms, although some outliers exist e.g., a(749) = 2251. When n starts with the digit 9, the values are somewhat more varied.
The maximum possible value for any term is the concatenation of n+1 and n, see the example for a(6) below. However except for a(6) and a(8), for the terms studied this only occurs four times for every order of magnitude increase in n, namely the four numbers consisting of all 9's except for the final digit of 0, 2, 6, or 8.
The first duplicate term is a(5) = a(18) = 37. There are 234 duplicates in the first 10000 terms.

			a(1) != 1 as "1"+"1"+"2" = 112 is not divisible by "1"+"2" = 12.
a(1) != 2 as "1"+"1"+"2" = 122 is not divisible by "1"+"2" = 12.
a(1) = 3 as "1"+"3"+"2" = 132 is divisible by "1"+"2" = 12.
a(5) = 37 as "5"+"37"+"6" = 5376 is divisible by "5"+"6" = 56.
a(6) = 76 as "6"+"76"+"7" = 6767 is divisible by "6"+"7" = 67. This is the first time the maximum possible value is required.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A001704, A215027, A248378.

cp's OEIS Frontend

A001704 a(n) = n concatenated with n + 1.

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A215028 a(1) = 1; for n >= 1, a(n+1) = (concatenation of n+1 and n) - a(n).

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A371144 The smallest number such that the concatenation of n, a(n), n+1 is divisible by the concatenation of n and n+1.

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