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 A260071 Primes p such that sigma(p) = sigma(p+1) - sigma(p-1). 1
 2, 3, 23, 970388922263, 991817878343, 1677028870823 (list; graph; refs; listen; history; text; internal format)
 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 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 HellstrÃ¶m, 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

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)