A262935 Increasing distances of lonely twin primes pairs to nearest prime.
1, 2, 4, 6, 10, 12, 16, 18, 28, 30, 34, 42, 46, 48, 58, 88, 90, 94, 124, 130, 136, 154, 162, 168, 172, 178, 202, 216, 258, 264, 294, 342, 352, 354, 364, 366, 370, 378, 396, 408
Offset: 1
Keywords
Examples
(3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=1. (5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=2. (11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=4.
Programs
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PARI
{m=0; q=5; s=3; t=2; forprime(p=6, 10^9, if((q-s==2) && (min(p-q, s-t)>m), m=min(p-q, s-t); print1(m, ", ") ); t=s; s=q; q=p;)}
Formula
a(n) = d if ( (p(i+1) = p(i)+2) AND (d = min(p(i+2)-p(i+1), p(i)-p(i-1)) > a(n-1)) ), where a(0) = 0, p(k) = prime(k) = A000040(k).
Comments