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%I #26 Sep 08 2022 08:46:13
%S 2,3,23,970388922263,991817878343,1677028870823
%N Primes p such that sigma(p) = sigma(p+1) - sigma(p-1).
%C Primes from A076530 (numbers n such that sigma(n) = sigma(n+1) - sigma(n-1)).
%C Also primes from sequence A260420 = (2, 3, 23, 14927, 31049, 69107, 246263, 5860169, ...): numbers n such that n+1 = sigma(n+1) - sigma(n-1)).
%C If a number from A246852(n) + 1 is a prime p, then p is in the sequence.
%C If a(7) exists, it must be bigger than 10^13.
%e 23 is in the sequence because sigma(24) - sigma(22) = 60 - 36 = 24 = sigma(23).
%o (Magma) [n: n in [1..1000000] | IsPrime(n) and SumOfDivisors(n) eq ((SumOfDivisors(n+1)) - (SumOfDivisors(n-1)))]
%o (Magma) [n: n in [A076530(n)] | IsPrime(n)]
%o (PARI) is_ok(index)=my(p=prime(index)); p+1==sigma(p+1)-sigma(p-1);
%o main(size)=my(v=vector(size),index=1);for(i=1,size,while(!is_ok(index),index++);v[i]=prime(index);index++); v \\ _Anders Hellström_, Jul 14 2015
%o (PARI) has(p)=p+1==sigma(p+1)-sigma(p-1)
%o select(has, primes(1000)) \\ _Charles R Greathouse IV_, Jul 22 2015
%Y Cf. A000203, A076530, A246852.
%K nonn,more,hard
%O 1,1
%A _Jaroslav Krizek_, Jul 14 2015
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