A276782 Where record values occur in A276781, when starting from A276781(2)=1.

2, 6, 15, 22, 36, 58, 95, 96, 147, 148, 209, 210, 305, 306, 901, 902, 903, 904, 905, 906, 1149, 1150, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 1360, 5621, 5622, 8499, 8500, 9585, 9586, 15719, 15720, 15721, 15722, 15723, 15724, 15725, 15726, 19653, 19654, 19655, 19656, 19657, 19658, 19659, 19660, 31449

Offset: 1

Author

N. J. A. Sloane, Sep 29 2016

Keywords

• nonn

Comments

Terms at the end of each run, that is, terms k that are not followed by k+1 (i.e., this excludes terms like 95, 147, 209, 901 .. 905, 1149, ...) form a subsequence of A181062. - Antti Karttunen, Jan 20 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..210 (terms 1..72 from Chai Wah Wu)
• Christophe Soulé, Le triangle de Pascal et ses propriétés, Lecture, Soc. Math. de France, Feb 13 2008.

Crossrefs

Cf. A181062, A276781.

Programs

Maple

A276781 := proc(n)
    local b,k;
    for b from 0 to floor(n/2+1) do
        igcd(seq(binomial(n,k),k=b..n-b)) ;
        if % > 1 then
            return b ;
        end if;
    end do:
end proc:
am := -1 ;
for n from 2 do
    an := A276781(n) ;
    if an > am then
        printf("%d,\n",n) ;
        am := an ;
    end if;
end do: # R. J. Mathar, Sep 30 2016

Mathematica

Function[t, First@ Position[t, #] & /@ Range@ Max@ t][{0}~Join~Table[b = 1; While[GCD @@ Map[Binomial[n, #] &, Range[b, n - b]] == 1, b++]; b, {n, 2, 1500}]] // Flatten (* Michael De Vlieger, Oct 03 2016 *)

PARI

A276781(n) = if(1==n,1,forstep(k=n,1,-1,if(isprimepower(k),return(1+n-k))));
m=0; k=0; n=1; while(k<210,n++; if((t=A276781(n))>m, m=t; k++; print1(n, ", "))); \\ Antti Karttunen, Jan 29 2020

Extensions

a(11)-a(30) from R. J. Mathar, Sep 30 2016

More terms from Chai Wah Wu, Oct 02 2016

Definition amended because of the changed definition of A276781, while keeping the terms same as before. - Antti Karttunen, Jan 29 2020