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

1,5

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

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*)

Prog

(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

Crossrefs

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

Cf. A034868, A010051.

Sequence in context: A121446 A302196 A340598 * A283220 A101326 A265391

Adjacent sequences: A258190 A258191 A258192 * A258194 A258195 A258196

Keyword

nonn

Author

Vladimir Shevelev, May 23 2015

Extensions

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

Status

approved