A212848 Least prime factor of n-th central trinomial coefficient (A002426).

1, 1, 3, 7, 19, 3, 3, 3, 3, 43, 7, 3, 113, 73, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 17, 3, 719, 7, 3, 3, 3, 3, 967, 9539, 3, 17, 47, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19

Offset

0,3

Comments

A002426(n) is prime for n = 2, 3, 4, no more through 10^5. A002426 is semiprime iff A102445(n) = 2 (as is the case for n = 5, 6, 7, 9, 10, 12, 13).

Links

Robert Israel, Table of n, a(n) for n = 0..729

Formula

a(n) = A020639(A002426(n)).

Example

a(9) = 43 because A002426(9) = 3139 = 43 * 73.

Maple

A002426:= gfun:-rectoproc({(n+2)*a(n+2)-(2*n+3)*a(n+1)-3*(n+1)*a(n) = 0, a(0)=1, a(1)=1}, a(n), remember):
lpf:= proc(n) local F;
    F:= map(proc(t) if t[1]::integer then t[1] else NULL fi end proc,
       ifactors(n, easy)[2]);
    if nops(F) > 0 then min(F)
    else min(numtheory:-factorset(n))
    fi
end proc:
lpf(1):= 1:
map(lpf @ A002426, [$0..100]); # Robert Israel, Jun 20 2017

Mathematica

a = b = 1; t = Join[{a, b}, Table[c = ((2 n - 1) b + 3 (n - 1) a)/n; a = b; b = c; c, {n, 2, 100}]]; Table[FactorInteger[n][[1, 1]], {n, t}] (* T. D. Noe, May 30 2012 *)

Prog

(PARI) a(n) = my(x=polcoeff((1 + x + x^2)^n, n)); if (x==1, 1, vecmin(factor(x)[, 1])); \\ Michel Marcus, Jun 20 2017

Crossrefs

Cf. A000040, A002426, A020639, A102445, A212791.

Sequence in context: A173449 A270519 A361087 * A217371 A088629 A075609

Adjacent sequences: A212845 A212846 A212847 * A212849 A212850 A212851

Keyword

nonn,easy

Author

Jonathan Vos Post, May 28 2012

Status

approved