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

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

Offset

1,2

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

Links

M. F. Hasler, Table of n, a(n) for n = 1..36

FactorDB, (121*10^(4*n-19) - 1002*10^(4*n-28) - 2*10^(2*n-9) + 879*10^10 + 121)/99^2.

Formula

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

Example

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).

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A140373 A316191 A003020 * A229612 A297797 A210321

Adjacent sequences: A075021 A075022 A075023 * A075025 A075026 A075027

Keyword

base,nonn

Author

Amarnath Murthy, Sep 01 2002

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

Status

approved