A258193 Define a<+>b = odd part(odd part(a) + odd part(b)), where odd part(n) = A000265(n); a(n) is the smallest prime of the form <+>_{0<=i<=k} binomial (n,i), or a(n)=0 if there is no such a prime (see comment).

0, 0, 0, 0, 3, 3, 11, 0, 5, 3, 3, 17, 7, 23, 53, 29, 13, 5, 5, 3, 11, 3, 3, 823, 13, 7, 7, 457, 109, 109, 233, 2267, 17, 59, 151, 5, 19, 5, 5, 3, 113, 11, 11, 3, 23, 3, 3, 71, 43, 13, 13, 7, 179, 7, 7, 193, 29, 2137, 863, 443, 31, 5498157739, 977, 163

Offset: 1

Author

Vladimir Shevelev, May 23 2015

Keywords

• nonn

Comments

f(n)=<+>_{0<=i<=n} c(i) is defined as the following: f(0)=c(0), f(n)=f(n-1)<+>c(n).

a(n)=0 for 1,2,3,4,8,82,107,...(cf. A258194)

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000265, A007318, A258126, A258127, A258194.

Cf. A034868, A010051.

Programs

Haskell

import Data.Function (on)
a258193 n = head $ (filter ((== 1) . a010051'') $
                    scanl1 (<+>) (a034868_row n)) ++ [0]
            where (<+>) = (a000265 .) . on (+) a000265
-- Reinhard Zumkeller, Jun 20 2015

Mathematica

vSum[a_,b_]:=#[#[a]+#[b]]&[#/2^IntegerExponent[#,2]&];
Table[
First[Select[FoldList[vSum,First[#],Rest[#]]&[Map[Binomial[n,#]&,Range[0,n]]],PrimeQ]/.{}->{0}],{n,100}] (*Peter J. C. Moses, May 23 2015*)

Extensions

More terms from Peter J. C. Moses, May 23 2015