A068635 Smaller of the first twin pair to yield a twin pair chain of length n.
3, 5, 211049, 253679, 41887255409, 73768891456259
Offset: 1
Keywords
Examples
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; ...
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.
Programs
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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))))))
Comments