A075024 - OEIS

%I #41 Mar 26 2022 17:45:05

%S 1,11,37,101,271,37,4649,137,333667,12345678910987654321,

%T 17636684157301569664903,2799473675762179389994681,

%U 2354041513534224607850261,2068140300159522133,498056174529497,112240064764214229701,4188353169004802474320231191377

%N a(n) is the largest prime divisor of the number A173426(n) = concatenate(1,2,...,n-1,n,n-1,...,2,1).

%C Also for 1 < n < 10, a(n) is the common prime divisor for all A010785(m) which consist of n digits. - _Alexander R. Povolotsky_, Jun 05 2014, corrected by _M. F. Hasler_, Jul 30 2015

%C According to the definition (and given terms), this is the greatest prime factor (A006530) of A173426 and not of A002477, as an earlier formula asserted and which may have been an assumption of the preceding comment. - _M. F. Hasler_, Jul 29 2015

%H M. F. Hasler, <a href="/A075024/b075024.txt">Table of n, a(n) for n = 1..36</a>

%H FactorDB, <a href="http://factordb.com/index.php?query=%28121*10%5E%284*n-19%29+-+1002*10%5E%284*n-28%29+-+2*10%5E%282*n-9%29+%2B+879*10%5E10+%2B+121%29%2F99%5E2&amp;perpage=60">(121*10^(4*n-19) - 1002*10^(4*n-28) - 2*10^(2*n-9) + 879*10^10 + 121)/99^2</a>.

%F a(n) = A006530(A173426(n)). - _Michel Marcus_, Jun 05 2014, corrected by _M. F. Hasler_, Jul 29 2015

%e a(5) = 271 as 123454321 = 41*41*271*271.

%e a(25) = 12471243489559387823527232424981012432152516319410549 is the larger factor of the semiprime A173426(24) = A075023(25) * a(n).

%t Table[FactorInteger[FromDigits[Join[Flatten[IntegerDigits/@Range[ n]], Flatten[ IntegerDigits/@Range[n-1,1,-1]]]]][[-1,1]],{n,20}] (* _Harvey P. Dale_, May 20 2016 *)

%o (PARI) a(n) = {if (n == 1, return (1)); s = ""; for (i=1, n, s = concat(s, Str(i));); forstep (i=n-1, 1, -1, s = concat(s, Str(i));); f = factor(eval(s)); f[#f~, 1];} \\ _Michel Marcus_, Jun 05 2014

%o (PARI) A075024(n)=A006530(A173426(n)) \\ A006530 should provide efficient code and also covers the case n=1. - _M. F. Hasler_, Jul 29 2015

%Y Cf. A075019, A075020, A075021, A075022, A075023.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 01 2002

%E More terms from _Sascha Kurz_, Jan 03 2003

%E a(16)-a(17) from _Michel Marcus_, Jun 05 2014

%E More terms from _M. F. Hasler_, Jul 29 2015