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 A208455 #25 Aug 04 2025 18:41:36
%S A208455 5516281,16831081,18164161,29743561,51755761,148057561,153742681,
%T A208455 158918761,175472641,189614881,212808961,297279361,298965241,
%U A208455 322030801,467313841,527428441,661686481,668745001,751524481,808214401
%N A208455 Primes p such that (p+k)/(k+1) is a prime number for k=1,...,5.
%C A208455 Subsequence of A071368 consisting of elements ending in the digit 1. (Proof: Let n=10k+1, {n,n+1,...,n+5}={P1,2*P2,...,6*P6} with P1,...,P6 prime. Obviously n+4=10k+5=5*P5. Since n+1==n+5 (mod 4), none of these two can be 4*P4. Thus, n+3=4*P4, whence n==P4 (mod 3) and n cannot be 3*P3. Therefore n=P1 and n+2=3*P3. Then n+5 is an even multiple of 3, n+5=6*P6, and n+1=2*P2 is the only remaining choice.)
%C A208455 Also: The subsequence of p in A204592 such that (p+5)/6 is a prime number. All terms are congruent to 1 modulo 2520 = A003418(9) = 7!/2 = 5*7*8*9.
%H A208455 M. F. Hasler, <a href="/A208455/b208455.txt">Table of n, a(n) for n = 1..1000</a>
%t A208455 Select[Range[1,810*10^6,2520],PrimeQ[#]&&AllTrue[Table[(#+k)/(k+1),{k,5}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 21 2015 *)
%o A208455 (PARI) {my(p=1); until(,isprime(p+=2520) || next; for(j=2, 6, isprime(p\j+1)||next(2)); print1(p","))}
%o A208455 (PARI) is_A208455(p,c=6)={ isprime(p) || return; for(j=2, c, isprime(p\j+1) || return); 1 }
%Y A208455 Cf. A093553. A207825 is a subsequence.
%K A208455 nonn
%O A208455 1,1
%A A208455 _M. F. Hasler_, Feb 27 2012
%E A208455 Value of A208455(1000) = 147435621481 = 58506199*2520+1 confirmed by Zak Seidov.