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a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of n, n-1, n-2, n-3, ... down to 1.
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%I #24 May 26 2022 09:52:29

%S 1,7,107,149,953,218107,402859,4877,379721,54421,370329218107,

%T 5767189888301,237927839,1728836281,136133374970881,1190788477118549,

%U 677181889,399048049,40617114482123,629639170774346584751,2605975408790409767,65372140114441

%N a(1) = 1; for n>1, a(n) = the largest prime divisor of the number C(n) formed from the concatenation of n, n-1, n-2, n-3, ... down to 1.

%H Daniel Suteu, <a href="/A075021/b075021.txt">Table of n, a(n) for n = 1..106</a>

%F a(n) = A006530(A000422(n)). - _Daniel Suteu_, May 26 2022

%e a(4)= 149 as 149 is the largest prime divisor of 4321 =29*149

%t b = {}; a = {}; Do[w = RealDigits[n]; w = First[w];Do[AppendTo[a, w[[Length[w] - k + 1]]], {k, 1, Length[w]}];p = FromDigits[Reverse[a]];AppendTo[b, First[Last[FactorInteger[p]]]], {n, 1, 21}]; b (* _Artur Jasinski_, Apr 04 2008 *)

%t Table[FactorInteger[FromDigits[Flatten[IntegerDigits/@Range[n,1,-1]]]] [[-1,1]],{n,20}] (* _Harvey P. Dale_, Dec 14 2020 *)

%o (PARI) a(n) = if(n==1, 1, vecmax(factor(eval(concat(apply(k->Str(n-k+1), [1..n]))))[, 1])); \\ _Daniel Suteu_, May 26 2022

%Y Cf. A006530, A000422, A075019, A075020, A075022.

%Y Cf. A104759, A116504, A007908, A116505, A104759, A138789, A138790, A138957, A138960, A138961, A138962.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 01 2002

%E More terms from _Sascha Kurz_, Jan 03 2003

%E Name edited by _Felix Fröhlich_, May 26 2022