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 A247821 #24 Sep 08 2022 08:46:09 %S A247821 2,1334,1969,28669,86006,126961,338603654,536801281, %T A247821 366479720500691270,375344017599431990,500461553802019261, %U A247821 554079264075351985 %N A247821 Numbers k such that sigma(sigma(2k-1)) is a prime p. %C A247821 Numbers n such that A000203(A000203(2n-1)) = A000203(A008438(n-1)) = A051027(2n-1) is a prime p. %C A247821 Corresponding values of primes p are 7, 8191, 8191, 131071, 524287, 524287, ... (= A247822). Conjecture: The primes p are Mersenne primes (A000668). %C A247821 sigma(sigma(2*a(9)-1)) > 10^16. %C A247821 If the above conjecture is true, the next terms are 366479720500691270, 375344017599431990, 500461553802019261, 554079264075351985, 98375588019240949991670086, ... . - _Hiroaki Yamanouchi_, Oct 01 2014 %C A247821 a(13) > 5*10^18. - _Giovanni Resta_, Feb 14 2020 %F A247821 a(n) = (A247838(n) +1) / 2. %F A247821 a(n)-1 = numbers n such that sigma(sigma(2n+1)) is a prime p: 1, 1333, 1968, 28668, 86005, 126960, ... %e A247821 Number 1334 is in sequence because sigma(sigma(2*1334-1)) = sigma(sigma(2667)) = sigma(4096) = 8191, i.e., prime. %t A247821 Select[Range[10^6], PrimeQ[DivisorSigma[1, DivisorSigma[1, 2 # - 1]]] &] (* _Robert Price_, May 17 2019 *) %o A247821 (Magma) [n: n in [1..10000000] | IsPrime(SumOfDivisors(SumOfDivisors(2*n-1)))] %o A247821 (PARI) %o A247821 for(n=1,10^7,if(ispseudoprime(sigma(sigma(2*n-1))),print1(n,", "))) \\ _Derek Orr_, Sep 29 2014 %Y A247821 Cf. A000203, A008438, A247790, A247791, A247820, A247822, A247823, A247954. %K A247821 nonn,more %O A247821 1,1 %A A247821 _Jaroslav Krizek_, Sep 28 2014 %E A247821 a(7)-a(8) from _Hiroaki Yamanouchi_, Oct 01 2014 %E A247821 a(9)-a(12) from _Giovanni Resta_, Feb 14 2020