A075023 - OEIS

%I #19 Jul 31 2015 00:46:28

%S 1,11,3,11,41,3,239,11,3,12345678910987654321,7,3,1109,7,3,71,7,3,251,

%T 7,3,70607,7,3,989931671244066864878631629,7,3,149,7,3,827,7,3,197,7,

%U 3,39907897297,7,3,17047,7,3,191,7,3,967,7,3,139121,7,3,109,7,3,5333,7,3

%N a(n) = the smallest prime divisor of A173426(n) = concatenation of (1, 2, 3,..., n, n-1, ..., 1) for n > 1; a(1) = 1.

%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) = A020639(A173426(n)). a(3n) = 3 for all n > 0. a(3n-1) = 7 for 3 < n < 34. - _M. F. Hasler_, Jul 29 2015

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

%e a(25) = 989931671244066864878631629 is the smaller factor of the semiprime A173426(24) = a(25) * A075023(25).

%e A173426(37) = 39907897297 * P58 * P59, where Pxx are primes with xx digits, therefore a(37) = 39907897297.

%o (PARI) A075023(n)=A020639(A173426(n)) \\ Efficient code for computing the least prime factor should be developed in A020639. For n = 37, use \g3 (debugging level 3) to see the lpf within milliseconds, while factorization would take hours. - _M. F. Hasler_, Jul 29 2015

%Y Cf. A075019, A075020, A075021, A075022, A075024.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 01 2002

%E More terms from _Sascha Kurz_, Jan 03 2003

%E Terms beyond a(24) from _M. F. Hasler_, Jul 29 2015