OFFSET
1,1
COMMENTS
Keller proved that the occurrence of 2 consecutive Woodall numbers that are divisible by the same prime is restricted to primes p with even h(p), the order of 2 mod p, and that there are an infinity of such pairs.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..350
Wilfrid Keller, New Cullen Primes, Mathematics of Computation, Vol. 64, No. 212 (October 1995), pp. 1733-1741.
FORMULA
EXAMPLE
11 is the 3rd prime p with even order of 2 mod p. A003261(k)=k*2^k-1 is divisible by 11 for k = 16,48,61,64,65,73,79,100,... The first occurrence of 2 consecutive numbers is 64 and 65, thus a(3) = 64.
MATHEMATICA
a = {}; For[p=0, p<=11699, p++; If[!PrimeQ[p], Continue[]]; h=MultiplicativeOrder[2, p]; If[!EvenQ[h], Continue[]]; n=(h/2+1)*p-2; a = AppendTo[a, n]]; a
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 20 2017
STATUS
approved