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A212848 Least prime factor of n-th central trinomial coefficient (A002426). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A079898 A173449 A270519 * A217371 A088629 A075609

Adjacent sequences:  A212845 A212846 A212847 * A212849 A212850 A212851

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, May 28 2012

STATUS

approved

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Last modified April 24 20:29 EDT 2019. Contains 322446 sequences. (Running on oeis4.)