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

2, 3, 23, 970388922263, 991817878343, 1677028870823

Offset

1,1

Comments

Primes from A076530 (numbers n such that sigma(n) = sigma(n+1) - sigma(n-1)).

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)).

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.

Links

Table of n, a(n) for n=1..6.

Example

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

Prog

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

Crossrefs

Cf. A000203, A076530, A246852.

Sequence in context: A203015 A260420 A241661 * A115031 A030418 A329456

Adjacent sequences: A260068 A260069 A260070 * A260072 A260073 A260074

Keyword

nonn,more,hard

Author

Jaroslav Krizek, Jul 14 2015

Status

approved