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A349822 Irregular triangle T(n,b) (n >= 3, 2 <= b <= A230624(n)/2+1) read by rows. Let m = A230624(n). Then T(n,b) is the smallest nonnegative number k such that k+S_b(k)=m, where S_b(k) is the sum of the digits of k in base b. 1
7, 7, 8, 7, 5, 11, 11, 10, 9, 12, 10, 7, 19, 17, 20, 17, 16, 17, 18, 15, 20, 16, 11, 35, 34, 31, 33, 29, 31, 33, 31, 28, 29, 30, 25, 32, 26, 34, 27, 36, 28, 19, 58, 58, 55, 57, 56, 55, 52, 51, 49, 51, 53, 49, 57, 52, 46, 47, 48, 49, 50, 41, 52, 42, 54, 43, 56, 44, 58, 45, 60, 46, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

T(n,b) must be nonzero for all b >= 2, and so this triangle is actually the upper left corner of an array with infinitely long rows (it is believed that there are also infinitely many rows).

Since T(n,b) = m/2 for all b > m/2, we may truncate row n after m/2 terms. The rows do not change beyond that point.

LINKS

Table of n, a(n) for n=3..75.

EXAMPLE

Triangle begins as follows:

   n    m   Row n

   3   10   [7, 7, 8, 7, 5],

   4   14   [11, 11, 10, 9, 12, 10, 7],

   5   22   [19, 17, 20, 17, 16, 17, 18, 15, 20, 16, 11],

   6   38   [35, 34, 31, 33, 29, 31, 33, 31, 28, 29, 30, 25, 32, 26, 34, 27, 36, 28, 19],

   7   62   [58, 58, 55, 57, 56, 55, 52, 51, 49, 51, 53, 49, 57, 52, 46, 47, 48, 49, 50, 41, 52, 42, 54, 43, 56, 44, 58, 45, 60, 46, 31],

   8   94   [90, 89, 89, 87, 87, 83, 89, 79, 83, 82, 80, 77, 86, 82, 77, 79, 81, 74, 85, 77, 89, 80, 70, 71, 72, 73, 74, 75, 76, 77, 78, 63, 80, 64, 82, 65, 84, 66, 86, 67, 88, 68, 90, 69, 92, 70, 47],

...

For n = 3, m = A230264(3) = 10, and row 3 of the triangle is [7, 7, 8, 7, 5], corresponding to the identities (where x_b is the base-b expansion of x):

   10 = 111_2 + 3 = 7 + 3,

      = 21_3 + 3 = 7 + 3

      = 20_4 + 2 = 8 + 2

      = 12_5 + 3 = 7 + 3

      = 5_b + 5  = 5 + 5 for all b >= 6.

CROSSREFS

Cf. A230624.

Sequence in context: A198992 A201668 A021853 * A092616 A260634 A294968

Adjacent sequences:  A349819 A349820 A349821 * A349823 A349824 A349825

KEYWORD

nonn,tabf,base

AUTHOR

N. J. A. Sloane, Dec 30 2021

STATUS

approved

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Last modified May 28 07:30 EDT 2022. Contains 354112 sequences. (Running on oeis4.)