A260420 -id:A260420 - cp's OEIS frontend

A260071 Primes p such that sigma(p) = sigma(p+1) - sigma(p-1).

2, 3, 23, 970388922263, 991817878343, 1677028870823

Offset: 1

Jaroslav Krizek, Jul 14 2015

Primes from A076530 (numbers n such that sigma(n) = sigma(n+1) - sigma(n-1)).
Also primes from sequence A260420 (numbers n such that sigma(n+1) - sigma(n-1) = n+1).
If a number from A246852(n) + 1 is a prime p, then p is in the sequence.
If a(7) exists, it must be bigger than 10^13.

			23 is in the sequence because sigma(24) - sigma(22) = 60 - 36 = 24 = sigma(23).

Cf. A000203, A076530, A246852.

[n: n in [1..1000000] | IsPrime(n) and SumOfDivisors(n) eq ((SumOfDivisors(n+1)) - (SumOfDivisors(n-1)))];

Magma
```
[n: n in [A076530(n)] | IsPrime(n)];
```

is_ok(index)=my(p=prime(index)); p+1==sigma(p+1)-sigma(p-1);
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

has(p)=p+1==sigma(p+1)-sigma(p-1)
select(has, primes(1000)) \\ Charles R Greathouse IV, Jul 22 2015

cp's OEIS Frontend

A260071 Primes p such that sigma(p) = sigma(p+1) - sigma(p-1).

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