A182402 -id:A182402 - cp's OEIS frontend

A226029 First differences of A182402.

1, 1, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 8, 11, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 39, 13, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Reinhard Zumkeller, May 26 2013

nonn

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

Cf. A182402, A226030.

a226029 n = a226029_list !! (n-1)
a226029_list = zipWith (-) (tail a182402_list) a182402_list

a(A226030(n)) = n and a(m) <> n for m < A226030(n).

a(n) = A182402(n+1) - A182402(n). - Michel Marcus, Jan 26 2022

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

Original entry on oeis.org

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

cp's OEIS Frontend

A226029 First differences of A182402.

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