A075023 a(n) = the smallest prime divisor of A173426(n) = concatenation of (1, 2, 3,..., n, n-1, ..., 1) for n > 1; a(1) = 1.
1, 11, 3, 11, 41, 3, 239, 11, 3, 12345678910987654321, 7, 3, 1109, 7, 3, 71, 7, 3, 251, 7, 3, 70607, 7, 3, 989931671244066864878631629, 7, 3, 149, 7, 3, 827, 7, 3, 197, 7, 3, 39907897297, 7, 3, 17047, 7, 3, 191, 7, 3, 967, 7, 3, 139121, 7, 3, 109, 7, 3, 5333, 7, 3
Offset: 1
Examples
a(5) = 41 as 123454321 = 41*41*271*271. a(25) = 989931671244066864878631629 is the smaller factor of the semiprime A173426(24) = a(25) * A075023(25). A173426(37) = 39907897297 * P58 * P59, where Pxx are primes with xx digits, therefore a(37) = 39907897297.
Programs
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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
Formula
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
Extensions
More terms from Sascha Kurz, Jan 03 2003
Terms beyond a(24) from M. F. Hasler, Jul 29 2015