This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152657 #6 Sep 08 2022 08:45:39 %S A152657 2,3,59,83,107,127,157,163,167,173,179,181,191,193,197,199,211,223, %T A152657 239,241,263,311,313,317,331,337,347,349,353,373,379,383,419,421,431, %U A152657 433,439,443,467,479,487,503,509,521,523,541,563,577,587,593,599,601,617 %N A152657 Secluded primes. %C A152657 A prime p is called secluded if it is not member of a chain of primes. A sequence of consecutive primes prime(k), ..., prime(k+r), r >= 1, is called a chain of primes if i*prime(i) + (i+1)*prime(i+1)* is prime for i from k to k+r-1. %H A152657 Klaus Brockhaus, <a href="/A152657/b152657.txt">Table of n, a(n) for n=1..10000</a> %e A152657 16*prime(16) + 17*prime(17) = 16*53 + 17*69 = 1851 = 3*617 is not prime; 17*prime(17) + 18*prime(18) = 17*59 + 18*61 = 2101 = 11+191 is not prime. Hence prime(17) = 59 is secluded. %o A152657 (Magma) [ p: n in [1..113] | (n eq 1 or not IsPrime((n-1)*NthPrime(n-1)+k)) and not IsPrime(k+(n+1)*NthPrime(n+1)) where k is n*p where p is NthPrime(n) ]; %Y A152657 Cf. A152117 (n*(n-th prime) + (n+1)*((n+1)-th prime)), A152658 (beginnings of maximal chains of primes), A119487 (primes of the form i*(i-th prime) + (i+1)*((i+1)-th prime), linking primes). %K A152657 nonn %O A152657 1,1 %A A152657 _Klaus Brockhaus_, Dec 10 2008