A158699 -id:A158699 - cp's OEIS frontend

A085890 7-smooth numbers (A002473) using digits in descending order. Zero is followed by a 9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 32, 54, 98, 210, 432

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

			432 is a member as 432= 2^4*3^3.

Intersection of A002473 and A158699.

Cf. A085889.

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 */

More terms from David Wasserman, Feb 10 2005

A247107 a(0) = 0, a(n) = previous term + repunit of length of previous term for n > 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 220, 331, 442, 553, 664, 775, 886, 997, 1108, 2219, 3330, 4441, 5552, 6663, 7774, 8885, 9996, 11107, 22218, 33329, 44440, 55551, 66662, 77773, 88884, 99995, 111106, 222217, 333328, 444439

Offset: 0

Dhilan Lahoti, Nov 30 2014

			98 = 9*10 + 8 -> 10*10 + 9 = 109.
109 = 1*100 + 0*10 + 9*1 -> 2*100 + 1*10 + 10*1 = 220.
a(42) = 44440 + (10^(floor(log_10(44440))+1)-1) / 9 = 44440 + (10^(4+1)-1) / 9 = 44440 + 99999/9 = 44440 + 11111 = 55551.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,10,-20,10).

Similar to A158699, but with simpler rules.

Cf. A002275, A055642.

a[0]=0; a[n_]:=FromDigits[IntegerDigits[a[n-1]]+1]; Array[a,50,0] (* Stefano Spezia, Sep 19 2024 *)

a(0) = 0, a(n) = a(n-1) + A002275(A055642(a(n-1))) for n>0.
From Jon E. Schoenfield, Nov 30 2014: (Start)
For n > 1, a(n) = a(n-1) + (10^(floor(log_10(a(n-1))) + 1) - 1) / 9.
For n > 0, a(n) = ((n-1) mod 9 + 1) * (10^D - 1) / 9 + 1 - D, where D = floor((n-1)/9) + 1. (There are exactly D digits in a(n).) (End)
G.f.: -(10*x^10-10*x^9+1)*x/((10*x^9-1)*(x-1)^2). - Alois P. Heinz, Nov 30 2014

cp's OEIS Frontend

A085890 7-smooth numbers (A002473) using digits in descending order. Zero is followed by a 9.

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