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A260071
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Primes p such that sigma(p) = sigma(p+1) - sigma(p-1).
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1
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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23 is in the sequence because sigma(24) - sigma(22) = 60 - 36 = 24 = sigma(23).
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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