A068635 Smaller of the first twin pair to yield a twin pair chain of length n.

3, 5, 211049, 253679, 41887255409, 73768891456259

Offset

1,1

Comments

PARI program written by Rick L. Shepherd.

If n is in the sequence and n>5 then Mod[n,30]=29. - Farideh Firoozbakht, Mar 26 2004

References

a(3) and a(4) found by Rick L. Shepherd and Don Reble; a(5) by David W. Wilson; a(6) by Don Reble.

Links

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

Example

5,7 form a twin pair, separated by the number 6. Their sum 12 is the separator of another twin pair, 11,13. _Their_ sum is not the separator of a further twin pair. (5,7),(11,13) is a chain of length 2. 5 is the lower of the smallest twin pair to generate a chain of this length, so a(2)=5.
Here are the actual chains (lesser of twin primes given): 3; 5 -> 11; 211049 -> 422099 -> 844199; 253679 -> 507359 -> 1014719 -> 2029439; 41887255409 -> 83774510819 -> 167549021639 -> 335098043279 -> 670196086559; ...

Prog

(PARI) for(n=1, 40000, if(prime(n+1)-prime(n)==2, s=prime(n+1)+prime(n); if(isprime(s-1)&&isprime(s+1), if(isprime(2*s-1)&&isprime(2*s+1), print(n, ", ", prime(n))))))

Crossrefs

Cf. A069142. Equals A069179 - 1.

Sequence in context: A319598 A353135 A126334 * A156695 A357258 A330251

Adjacent sequences: A068632 A068633 A068634 * A068636 A068637 A068638

Keyword

nonn

Author

Neil Fernandez, Apr 10 2002

Status

approved