A059043 -id:A059043 - cp's OEIS frontend

A138141 Numbers with digits in ascending order that differ exactly by 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 23, 34, 45, 56, 67, 78, 89, 123, 234, 345, 456, 567, 678, 789, 1234, 2345, 3456, 4567, 5678, 6789, 12345, 23456, 34567, 45678, 56789, 123456, 234567, 345678, 456789, 1234567, 2345678, 3456789, 12345678, 23456789, 123456789

Offset: 1

Omar E. Pol, Mar 19 2008

This finite sequence has 45 members. The last member is 123456789. There are 10-k members with k digits. See A052017 for primes in this sequence. All members with 3 or more digits are straight-line numbers A135643.

Cf. A052017, A059043, A135643, A138142.

Table[FromDigits/@Partition[Range[9],n,1],{n,9}]//Flatten (* Harvey P. Dale, Mar 19 2017 *)

a(n) = floor(((9*t^2 - 189*t + 18*n + 182) * (10^t - 1) - 18*t) / 162), where t = floor((21 - sqrt(369 - 8*n)) / 2). - Christopher J. Thomas, Feb 14 2024

A161760 Composites with consecutive (ascending) digits.

Original entry on oeis.org

4, 6, 8, 9, 12, 34, 45, 56, 78, 90, 123, 234, 345, 456, 567, 678, 789, 890, 901, 1234, 2345, 3456, 5678, 6789, 7890, 8901, 9012, 12345, 23456, 34567, 45678, 56789, 67890, 89012, 90123

Offset: 1

Claudio Meller, Jun 18 2009

R. J. Mathar, Table of n, a(n) for n = 1..200

A059043 - A006055 - 1

A215477 Semiprimes with consecutive (ascending) digits.

Original entry on oeis.org

4, 6, 9, 34, 123, 789, 901, 1234, 34567, 56789, 901234, 1234567, 7890123, 567890123, 12345678901, 345678901234567, 4567890123456789, 12345678901234567, 890123456789012345, 3456789012345678901, 456789012345678901234, 123456789012345678901234567, 1234567890123456789012345678901, 23456789012345678901234567890123

Offset: 1

Jonathan Vos Post, Aug 12 2012

This is to semiprimes A001358 as A006055 is to primes.

			a(9) = 34567 because it is semiprime 13 * 2659, and (3,4,5,6,7) are consecutive ascending digits.

Cf. A001358, A118697, A059043, A006055, A161760.

R:= 4, 6, 9: V:= [$1..9]:
for d from 2 to 50 do
V:= map(n -> 10*n + ((n+1) mod 10), V);
W:= select(t -> numtheory:-bigomega(t)=2, V);
R:= R, op(W);
od:
R; # Robert Israel, Nov 15 2023

Corrected and extended by R. J. Mathar, Aug 13 2012

A085889 7-smooth numbers (A002473) using digits in increasing order. 9 is followed by a zero.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 45, 56, 90, 567, 3456

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003

No more terms < 10^1000. Probably no more terms. - David Wasserman, Feb 10 2005

			567 is a member as 567 = 3^4*7.

Intersection of A002473 and A059043.

Cf. A085890.

hcn(n) = while (!(n%2), n \=2); while (!(n%3), n \=3); while (!(n%5), n \=5); while (!(n%7), n \=7); n == 1;
for (i = 0, 1000, for (j = 1, 9, my(n = sum(k = j, i + j, (k%10)*10^(i + j - k))); if (hcn(n), print1(n, ", ")))); /* David Wasserman, Feb 10 2005 */

3456 from David Wasserman, Feb 10 2005

cp's OEIS Frontend

A138141 Numbers with digits in ascending order that differ exactly by 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

A161760 Composites with consecutive (ascending) digits.

Views

Author

Keywords

Links

Crossrefs

A215477 Semiprimes with consecutive (ascending) digits.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Extensions

A085889 7-smooth numbers (A002473) using digits in increasing order. 9 is followed by a zero.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions