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Smallest m such that A226029(m) = n.
2

%I #25 Jan 27 2022 13:28:10

%S 1,3,15,46,4,448,1415,13,14143,44722,14,447215,45,4472137,14142137,

%T 140,141421357,447213596,1414213563,4472135956,14142135625,

%U 44721359551,141421356238,447213595501,1414213562374,4472135955001,14142135623732,44721359549997,141421356237311,447213595499959

%N Smallest m such that A226029(m) = n.

%C a(39) = 44. - _Michel Marcus_, Jan 26 2022

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

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

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a226030 = (+ 1) . fromJust . (`elemIndex` a226029_list)

%o (PARI) 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

%o 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

%Y Cf. A068092, A182402, A226029.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 26 2013

%E a(12)-a(18) from _Michel Marcus_, Jan 26 2022

%E More terms from _David A. Corneth_, Jan 26 2022