A090073 a(n) = least number m such that m-1, m+1 are twin primes, m=a*b and there are 2^n - 1 choices for (S, D) where S=a+b, D=a-b (a>b>1) and with both S and D primes.

18, 60, 1932, 43890, 62478570, 3827339670

Offset

1,1

Comments

Note that (m-1)^2+S^2=(m+1)^2+D^2.

If k is the number of distinct prime factors of m, then the maximum number of (S, D) values both primes is 2^(k-1)-1. 18, 60 and 1932 are the only terms of the sequence with all (S, D) values both primes. If we consider 1 to be prime (and pi(1)=0), then the first 3 terms are 6, 30, 462

Links

Table of n, a(n) for n=1..6.

Example

m=18,(m-1,m+1)=(17,19),{(S,D)}={(11,7)}
m=60,(m-1,m+1)=(59,61),{(S,D)}={(23,17),(19,11),(17,7)}
m=1932 7 (S,D) prime values
m=43890 15 (S,D) prime values....

Crossrefs

Sequence in context: A154563 A325043 A338536 * A327089 A016728 A232385

Adjacent sequences: A090070 A090071 A090072 * A090074 A090075 A090076

Keyword

hard,more,nonn

Author

Robin Garcia, Jan 21 2004

Status

approved