A075024 a(n) is the largest prime divisor of the number A173426(n) = concatenate(1,2,...,n-1,n,n-1,...,2,1); a(1) = 1.

1, 11, 37, 101, 271, 37, 4649, 137, 333667, 12345678910987654321, 17636684157301569664903, 2799473675762179389994681, 2354041513534224607850261, 2068140300159522133, 498056174529497, 112240064764214229701, 4188353169004802474320231191377

Offset: 1

Author

Amarnath Murthy, Sep 01 2002

Keywords

• base
• nonn

Comments

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

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

Examples

			a(5) = 271 as 123454321 = 41*41*271*271.
a(25) = 12471243489559387823527232424981012432152516319410549 is the larger factor of the semiprime A173426(24) = A075023(25) * a(n).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..58 (terms 1..36 from M. F. Hasler)
• FactorDB, (121*10^(4*n-19) - 1002*10^(4*n-28) - 2*10^(2*n-9) + 879*10^10 + 121)/99^2.

Crossrefs

Cf. A002477, A006530, A010785, A075019, A075020, A075021, A075022, A075023, A173426.

Programs

Mathematica

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 *)

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

PARI

A075024(n)=A006530(A173426(n)) \\ A006530 should provide efficient code and also covers the case n=1. - M. F. Hasler, Jul 29 2015

Formula

a(n) = A006530(A173426(n)). - Michel Marcus, Jun 05 2014, corrected by M. F. Hasler, Jul 29 2015

Extensions

More terms from Sascha Kurz, Jan 03 2003

a(16)-a(17) from Michel Marcus, Jun 05 2014

More terms from M. F. Hasler, Jul 29 2015