A226029 -id:A226029 - cp's OEIS frontend

A226030 Smallest m such that A226029(m) = n.

1, 3, 15, 46, 4, 448, 1415, 13, 14143, 44722, 14, 447215, 45, 4472137, 14142137, 140, 141421357, 447213596, 1414213563, 4472135956, 14142135625, 44721359551, 141421356238, 447213595501, 1414213562374, 4472135955001, 14142135623732, 44721359549997, 141421356237311, 447213595499959

Offset: 1

Reinhard Zumkeller, May 26 2013

nonn

a(39) = 44. - Michel Marcus, Jan 26 2022

Let k = ceiling(sqrt(2*10^m)). Then some terms are of the form k or k + 1. - David A. Corneth, Jan 27 2022

Cf. A068092, A182402, A226029.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a226030 = (+ 1) . fromJust . (`elemIndex` a226029_list)

nb(n) = {my(x=n*(n-1)/2+1, y=n*(n+1)/2, nx=#Str(x), ny=#Str(y), s=0); for (i=nx, ny, if (i==nx, if (i==ny, s+=(y+1-x)*i, s+=(10^i-x)*i), if (i==ny, s+=(y+1-10^(i-1))*i, s+=i*(10^(i+1)-10^i+1)););); s;} \\ A182402
a(n) = my(k=1, last=nb(k), new=nb(k+1)); while (new-last !=n, k++; last=new; new=nb(k+1)); k; \\ Michel Marcus, Jan 26 2022

A226029(a(n)) = n and A226029(m) <> n for m < a(n).

a(12)-a(18) from Michel Marcus, Jan 26 2022

More terms from David A. Corneth, Jan 26 2022

A182402 Total number of digits in n-th row of a triangle formed by the positive integers.

Original entry on oeis.org

1, 2, 3, 5, 10, 12, 14, 16, 18, 20, 22, 24, 26, 34, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 171, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232

Offset: 1

Dave Durgin, Jun 19 2012

Sequence is nonlinear at each decade transition; for example, row-5 transitions from single-digit (7) to double-digit (10) where sequence jumps (3) to (5); row-14 transitions from 2-digit (92) to 3-digit (105) where sequence jumps from (26) to (34).

The rows of nonlinearity are given by A068092. - Jon Perry, May 26 2013

			1; .................... (row 1 contains 1 digit)
2,   3; ............... (row 2 contains 2 digits)
4,   5,  6; ........... (row 3 contains 3 digits)
7,   8,  9, 10; ....... (row 4 contains 5 digits)
11, 12, 13, 14, 15; ... (row 5 contains 10 digits)

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A055642, A226029 (first differences).

Cf. A068092.

a182402 n = a182402_list !! (n-1)
a182402_list = map (sum . map a055642) $ t 1 [1..] where
   t i xs = ys : t (i + 1) zs where
     (ys, zs) = splitAt i xs
-- Reinhard Zumkeller, May 26 2013

f[n_] := Length@ Flatten[ IntegerDigits[ Range[n (n - 1)/2 + 1, n (n + 1)/2]]]; Array[f, 58] (* Robert G. Wilson v, Sep 04 2013 *)

a(n) = {my(x=n*(n-1)/2+1, y=n*(n+1)/2, nx=#Str(x), ny=#Str(y), s=0); for (i=nx, ny, if (i==nx, if (i==ny, s+=(y+1-x)*i, s+=(10^i-x)*i), if (i==ny, s+=(y+1-10^(i-1))*i, s+=i*(10^(i+1)-10^i+1)););); s;} \\ Michel Marcus, Jan 26 2022

def a(n): return len("".join(str(i) for i in range(n*(n+1)//2+1, (n+1)*(n+2)//2+1)))
print([a(n) for n in range(58)]) # Michael S. Branicky, Jan 26 2022

a(n) = A058183(A000217(n)) - A058183(A000217(n-1)), n >= 2. - Omar E. Pol, Jun 25 2012

Better definition from Omar E. Pol, Jun 25 2012

cp's OEIS Frontend

A226030 Smallest m such that A226029(m) = n.

Views

Author

Keywords

Comments

Crossrefs

Programs

Haskell

PARI

Formula

Extensions