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 A259564 #19 Oct 12 2020 12:25:28
%S A259564 5,7,11,30,133,160,415,527,883,1257,2025,2771,2775,6650,6932,13793,
%T A259564 19091,30695,32341,33722,36372,37944,40532,42141,47230,60986,77956,
%U A259564 82165,90564,111414,113106,136036,147573,148357,158279,169137,169604,171549,174540,187679
%N A259564 Numbers n such that the sum of the prime factors (including repeats) of prime(n)-1 and prime(n+1)-1 are the same.
%C A259564 Although there are more terms than A105403 so far, these numbers are still fairly uncommon.
%C A259564 Is this sequence infinite?
%e A259564 The prime factors of prime(30)-1 are 2,2,2,2,7 and the prime factors of prime(31)-1 are 2,3,3,7. The sum of entries in each of these lists is 15.
%t A259564 SequencePosition[Table[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ p-1]]],{p,Prime[Range[200000]]}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 12 2020 *)
%o A259564 (PARI) spff(n) = {my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2]);}
%o A259564 lista(nn) = {forprime(p=2, nn, if (spff(p-1)==spff(nextprime(p+1)-1), print1(primepi(p), ", ")););} \\ _Michel Marcus_, Jun 30 2015
%Y A259564 Cf. A001414, A105403, A259562.
%K A259564 nonn
%O A259564 1,1
%A A259564 _Otis Tweneboah_, _Pratik Koirala_, _Eugene Fiorini_, _Nathan Fox_, Jun 30 2015
%E A259564 More terms from _Alois P. Heinz_, Jun 30 2015
%E A259564 Name edited by _Zak Seidov_, Jul 02 2015