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

1,2

Links

Table of n, a(n) for n=1..57.

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A110774 A261411 A067063 * A363099 A205960 A302556

Adjacent sequences: A075020 A075021 A075022 * A075024 A075025 A075026

Keyword

base,nonn

Author

Amarnath Murthy, Sep 01 2002

Extensions

More terms from Sascha Kurz, Jan 03 2003

Terms beyond a(24) from M. F. Hasler, Jul 29 2015

Status

approved