A087779 a(n)=prime(x) is the smallest prime such that 1+(2^(12n+9))*prime(x) is divisible by prime(x+1).

19, 43, 67, 31, 2087, 29, 31, 89, 6359, 31, 29, 19, 31, 199, 1429, 29, 229, 641, 31, 41, 29, 31, 19, 89, 31, 29, 41, 31, 29573, 38729, 29, 89, 389, 19, 43103, 29, 31, 67, 929, 31, 29, 38729, 31, 89, 19, 29, 146543, 41, 31, 1193, 29, 31, 5077, 53, 31, 19, 449, 31, 701

Offset

0,1

Links

Table of n, a(n) for n=0..58.

Formula

a(n)=Min{p[x]; Mod[1+[2^(12n+9)].p[x], p[x+1]]=0}; a(n)=A087985[2^(9+12n)]

Example

n = 4: exponent = 4.12+9 = 57, 2^57 = 144115188075855872; a(4) = 2087 = p[315] because 1+144115188075855872.2087 = 300768397514311204865 = 2089.5.23.2593.14669.32914927 = p[316].m
Must a solution always exist? Difficult exponents are 193,253,...

Crossrefs

Cf. A087985.

Sequence in context: A095086 A095079 A238676 * A106950 A141438 A350051

Adjacent sequences: A087776 A087777 A087778 * A087780 A087781 A087782

Keyword

nonn

Author

Labos Elemer, Oct 06 2003

Extensions

More terms from David Wasserman, Jun 17 2005

Status

approved