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 A162565 #23 Feb 25 2025 09:00:31
%S A162565 3,5,7,13,17,19,31,37,41,43,61,67,73,79,97,101,103,109,113,127,139,
%T A162565 151,157,163,181,191,193,197,199,229,233,241,251,271,277,281,283,313,
%U A162565 317,337,349,353,373,379,401,409,421,431,433,439,457,461,463,523,541,547
%N A162565 Those primes p such that (p-q) divides (p-1), where q is the greatest prime < p.
%C A162565 A006512 (greater of twin primes) is a subsequence. - _Michel Marcus_, Feb 27 2019
%C A162565 Except for 11, A090609 is a subsequence. - _Davide Rotondo_, Feb 12 2025
%H A162565 Harvey P. Dale, <a href="/A162565/b162565.txt">Table of n, a(n) for n = 1..1000</a>
%e A162565 The 17th prime is 59 and the 18th prime is 61. (61-59) = 2, and 2 divides 61-1 = 60. So 61 is in the sequence.
%p A162565 A162565 := proc(n) local p,q; p := ithprime(n) ; q := prevprime(p) ; if (p-1) mod (p-q) = 0 then printf("%d,",p); fi; end: seq(A162565(n),n=2..200) ; # _R. J. Mathar_, Jul 13 2009
%t A162565 Transpose[Select[Partition[Prime[Range[110]],2,1],Divisible[#[[2]]-1, #[[2]] - #[[1]]]&]][[2]] (* _Harvey P. Dale_, Mar 18 2016 *)
%o A162565 (PARI) isok(p) = isprime(p) && !((p-1) % (p-precprime(p-1))); \\ _Michel Marcus_, Feb 12 2025
%Y A162565 Cf. A006512, A162566.
%K A162565 nonn
%O A162565 1,1
%A A162565 _Leroy Quet_, Jul 06 2009
%E A162565 More primes from _R. J. Mathar_, Jul 13 2009