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 A284037 #42 Mar 09 2025 12:30:10
%S A284037 11,13,19,23,37,47,53,73,97,107,163,193,383,487,577,863,1153,2593,
%T A284037 2917,4373,8747,995327,1492993,1990657,5308417,28311553,86093443,
%U A284037 6879707137,1761205026817,2348273369087,5566277615617,7421703487487,21422803359743,79164837199873
%N A284037 Primes p such that p-1 and p+1 have two distinct prime factors.
%C A284037 Either p-1 or p+1 must be of the form 2^i * 3^j, since among three consecutive numbers exactly one is a multiple of 3. - _Giovanni Resta_, Mar 29 2017
%C A284037 Subsequence of A219528. See the previous comment. - _Jason Yuen_, Mar 08 2025
%H A284037 Robert Israel, <a href="/A284037/b284037.txt">Table of n, a(n) for n = 1..51</a> (all terms < 10^75)
%F A284037 A001221(a(n)) = 1 and A001221(a(n) - 1) = A001221(a(n) + 1) = 2.
%e A284037 7 is not a term because n + 1 = 8 has only one prime factor.
%e A284037 23 is a term because it is prime and n - 1 = 22 has two distinct prime factors (2, 11) and n + 1 = 24 has two distinct prime factors (2, 3).
%e A284037 43 is not a term because n - 1 = 42 has three distinct prime factors (2, 3, 7).
%p A284037 N:= 10^20: # To get all terms <= N
%p A284037 Res:= {}:
%p A284037 for i from 1 to ilog2(N) do
%p A284037 for j from 1 to floor(log[3](N/2^i)) do
%p A284037 q:= 2^i*3^j;
%p A284037 if isprime(q-1) and nops(numtheory:-factorset((q-2)/2^padic:-ordp(q-2,2)))=1 then Res:= Res union {q-1} fi;
%p A284037 if isprime(q+1) and nops(numtheory:-factorset((q+2)/2^padic:-ordp(q+2,2)))=1 then Res:= Res union {q+1} fi
%p A284037 od od:
%p A284037 sort(convert(Res,list)); # _Robert Israel_, Apr 16 2017
%t A284037 mx = 10^30; ok[t_] := PrimeQ[t] && PrimeNu[t-1]==2==PrimeNu[t+1]; Sort@ Reap[Do[ w = 2^i 3^j; Sow /@ Select[ w+ {1,-1}, ok], {i, Log2@ mx}, {j, 1, Log[3, mx/2^i]}]][[2, 1]] (* terms up to mx, _Giovanni Resta_, Mar 29 2017 *)
%o A284037 (Sage) omega=sloane.A001221; [n for n in prime_range(10^6) if 2==omega(n-1)==omega(n+1)]
%o A284037 (Sage) sorted([2^i*3^j+k for i in (1..40) for j in (1..20) for k in (-1,1) if is_prime(2^i*3^j+k) and sloane.A001221(2^i*3^j+2*k)==2])
%o A284037 (PARI) isok(n) = isprime(n) && (omega(n-1)==2) && (omega(n+1)==2); \\ _Michel Marcus_, Apr 17 2017
%Y A284037 Cf. A000668, A001221, A005105, A005109, A033845, A058383, A067386, A092506, A215504, A219528, A275598.
%K A284037 nonn
%O A284037 1,1
%A A284037 _Giuseppe Coppoletta_, Mar 28 2017
%E A284037 a(33)-a(34) from _Giovanni Resta_, Mar 29 2017