A077216 Smallest prime(k) such that 2^n divides the product of composite numbers between prime(k) and prime(k+1) but 2^(n+1) does not.

2, 5, 3, 19, 7, 13, 23, 47, 31, 89, 139, 113, 199, 293, 631, 317, 1069, 509, 2503, 1129, 1759, 2039, 887, 1951, 4027, 3967, 2477, 2971, 3271, 6917, 4831, 5591, 10799, 5119, 14107, 9973, 1327, 39461, 16381, 20809, 11743, 15683, 61169, 52391, 33247, 45439

Offset

0,1

Links

Table of n, a(n) for n=0..45.

Example

a(0) = 2, a(1) = 5, a(2) = 3 a(5) = 13 as 2^5 = 32 divides 14*15*16 but 2^6=64 does not.

Mathematica

f[n_] := Block[{k = 1}, While[ Mod[Times @@ Select[ Range[Prime@k, Prime[k + 1]], ! PrimeQ@# &], 2^n] != 0 || Mod[Times @@ Select[ Range[Prime@k, Prime[k + 1]], ! PrimeQ@# &], 2^(n + 1)] == 0, k++ ]; Prime@k]; Table[ f[n], {n, 0, 45}] (* Robert G. Wilson v, Apr 06 2006 *)

Crossrefs

Sequence in context: A248576 A087228 A285743 * A227617 A309080 A058357

Adjacent sequences: A077213 A077214 A077215 * A077217 A077218 A077219

Keyword

nonn

Author

Amarnath Murthy, Nov 02 2002

Extensions

More terms from Robert G. Wilson v, Apr 06 2006

Status

approved