A069890 Smallest odd number k such that p(2m)-2p(m)=k has exactly n solutions (where p(m) = m-th prime).

23, 1, 19, 15, 209, 433, 657, 135, 435, 2715, 9525, 9639, 20757, 20493, 4389, 47025, 27555, 193875, 162435, 51405, 811497, 764547, 832995, 811485, 811515, 193755, 1233309, 811473, 15680805, 4247325, 10797675, 12945345, 15391761

Offset

0,1

Links

Table of n, a(n) for n=0..32.

Example

n=0: 23 is the smallest odd number without solutions: see A070774. For n=1, .., 8 the solutions are s1={3}, s2={41, 47}, s3={19, 23, 37}, s4={661, 769, 787, 811}, s5={1619, 1667, 1709, 1823, 1979}, s6={2777, 2843, 2851, 2861, 2897, 3251}, s7={439, 443, 449, 457, 487, 557, 593}, s8={1621, 1637, 1699, 1723, 1741, 1777, 1811, 1987}, expressed in terms of p(x) primes; either values of x and 2x indices or p(2x) are further computable. Odd numbers a(n) forming sequence corresponds to values of p(2x)-2p(x). E.g. p[2*Pi[s4]]=p[2x]={1531, 1747, 1783, 1831} and p[2x]-2p[x]]={209, 209, 209, 209} gives a(4)=209.

Crossrefs

Cf. A066066, A022457, A070773, A070774.

Sequence in context: A040548 A189048 A040549 * A040550 A040551 A157981

Adjacent sequences: A069887 A069888 A069889 * A069891 A069892 A069893

Keyword

nonn

Author

Labos Elemer, May 06 2002

Extensions

a(15)-a(32) from Donovan Johnson, Oct 27 2008

Status

approved