A080393 a(n) is the smallest integer such that A080383(a(n)) = n.

0, 1, 2, 3, 40, 5, 12, 25, 1122, 13, 420, 1103, 12324, 421, 4960, 11289, 232582, 4961, 16356, 107073

Offset: 1

Author

Labos Elemer, Mar 17 2003

Keywords

• nonn
• more

Comments

Parity of n and a(n) is opposite.

It is unknown whether all positive integers arise in A080383 or not.

a(22)=16357, a(23)=90306, a(26)=90307. - Vaclav Kotesovec, Sep 10 2019

For each n > 20 except 22, 23, and 26, a(n) > 10^6 (if it exists). - Jon E. Schoenfield, Sep 15 2019

Examples

			a(10)=13 because in A080383 10 appears first as the 13th term.
		

Crossrefs

Cf. A080383, A080384(1)=a(6), A080385(1)=a(7), A080386(1)=a(8), A080387(1)=a(10).

Programs

Mathematica

f[x_] := Count[Table[IntegerQ[Binomial[x, Floor[x/2]]/ Binomial[x, j]], {j, 0, n}], True]; t=Table[0, {20}]; Do[s=f[n]; If[s<21&&t[[s]]==0, t[[s]]=n], {n, 1, 1300}]; t

PARI

f(n) = my(b=binomial(n, n\2)); sum(i=0, n, (b % binomial(n, i)) == 0); \\ A080383
a(n) = my(k=0); while(f(k) != n, k++); k; \\ Michel Marcus, Aug 23 2019

Extensions

a(13)-a(16) from Michel Marcus, Aug 23 2019

a(17) from Jon E. Schoenfield, Sep 15 2019

a(18) from Michel Marcus, Aug 23 2019

a(19) from Vaclav Kotesovec, Sep 10 2019

a(20) from Jon E. Schoenfield, Sep 15 2019