A241845 a(1)=1; for n >1 a(n) is the smallest prime divisor of the number obtained from concatenation of 1 and the first n-1 composites.

1, 2, 2, 2, 37, 2, 2, 2, 5, 2, 2, 2, 27793, 2, 2, 3, 2, 29, 2, 2, 2, 19, 2, 5, 2, 2, 1468910121415161820212224252627283032333435363839, 2, 2, 2, 5, 2, 2, 3, 2, 127, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2

Offset

1,2

Comments

a(1)=1, and for n > 1 a(n) is the smallest prime divisor of the number obtained from the concatenation of A018252(j), j=1, ..., n. - Wolfdieter Lang, May 07 2014

Links

Jinyuan Wang, Table of n, a(n) for n = 1..185

Example

1 U 4 = 14 and its divisors are 1, 2, 7, 14. Then a(2) = 2.
14 U 6 = 146 and its divisors are 1, 2, 73, 146. Then a(3) = 2.
146 U 8 = 1468 and its divisors are 1, 2, 4, 734, 367, 1468. Then a(4) = 2.
1468 U 9 = 14689 and its divisors are 1, 37, 397, 14689. Then a(5) = 37. Etc.

Maple

with(numtheory):
T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, n; b:=1; print(1); for n from 2 to q do if not isprime(n) then b:=n+b*10^T(n); a:=sort([op(divisors(b))]); print(a[2]);
fi; od; end: P(10^6); # Paolo P. Lava, Apr 30 2014

Mathematica

Module[{nn=70, cmps}, cmps=Select[Range[nn], CompositeQ]; Join[ {1}, SelectFirst[ Divisors[#], PrimeQ]&/@FromDigits/@Table[ Join[ {1}, Flatten[ IntegerDigits/@Take[cmps, n]]], {n, Length[cmps]}]]] (* Harvey P. Dale, Jul 27 2021 *)

Crossrefs

Cf. A018252, A075019, A104644, A132934.

Sequence in context: A083148 A368204 A318166 * A254131 A339014 A175910

Adjacent sequences: A241842 A241843 A241844 * A241846 A241847 A241848

Keyword

nonn,base

Author

Paolo P. Lava, Apr 30 2014

Extensions

More terms from Jinyuan Wang, Jun 27 2020

Status

approved