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A249695 a(n)=0, if A249441(n)=0; otherwise, a(n) is the smallest i such that A249441(n)^2 divides binomial(n,i). 7
0, 0, 0, 0, 1, 0, 3, 0, 1, 2, 3, 0, 1, 6, 3, 7, 1, 2, 3, 4, 1, 6, 3, 0, 1, 2, 3, 12, 1, 6, 3, 5, 1, 2, 3, 4, 1, 6, 3, 8, 1, 2, 3, 12, 1, 6, 3, 21, 1, 2, 3, 4, 1, 6, 3, 24, 1, 2, 3, 12, 1, 6, 3, 1, 1, 2, 3, 4, 1, 6, 3, 8, 1, 2, 3, 12, 1, 6, 3, 16, 1, 2, 3, 4, 1, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

After a(0) = 0, A048278 gives the positions of seven other zeros in the sequence. - Antti Karttunen, Nov 04 2014

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

MAPLE

A249695 := proc(n)

    a41n := A249441(n) ;

    if a41n = 0 then

        return 0;

    end if;

    bi := 1;

    for i from 0 do

        if modp(bi, a41n^2)= 0 then

            return i;

        end if;

        bi := bi*(n-i)/(1+i) ;

    end do:

end proc: # R. J. Mathar, Nov 04 2014

MATHEMATICA

bb[n_] := Table[Binomial[n, k], {k, 1, (n - Mod[n, 2])/2}];

a41[n_] := If[MemberQ[{0, 1, 2, 3, 5, 7, 11, 23}, n], 0, For[p = 2, True, p = NextPrime[p], If[AnyTrue[bb[n], Divisible[#, p^2]&], Return[p]]]];

a[n_] := If[(a41n = a41[n]) == 0, 0, For[i = 1, True, i++, If[Divisible[ Binomial[n, i], a41n^2], Return[i]]]];

a /@ Range[0, 100] (* Jean-Fran├žois Alcover, Mar 27 2020 *)

PROG

(PARI)

A249695(n) = { forprime(p=2, 3, for(k=0, floor(n/2), if((0==(binomial(n, k)%(p*p))), return(k)))); return(0); } \\ Straightforward and unoptimized version. But fast enough for 10000 terms.

A249695(n) = { for(p=2, 3, my(o=0); for(k=1, n\2, o+=valuation((n-k+1)/k, p); if(o>1, return(k)))); return(0); } \\ This version is based on Charles R Greathouse IV's code for A249441.

for(n=0, 10000, write("b249695.txt", n, " ", A249695(n)));

\\ Antti Karttunen, Nov 04 2014

CROSSREFS

A249714 and A249715 give the record values and their positions.

Cf. A048278, A249441, A249722, A249723, A249726.

Differs from A249442 for the first time at n=9.

Sequence in context: A147755 A307195 A231188 * A136748 A235919 A229654

Adjacent sequences:  A249692 A249693 A249694 * A249696 A249697 A249698

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Nov 04 2014

STATUS

approved

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Last modified July 12 12:18 EDT 2020. Contains 335661 sequences. (Running on oeis4.)