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A219860
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a(n) is the smallest number greater than a(n-1) such that sigma(a(1)) + sigma(a(2)) + ... + sigma(a(n)) is prime.
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1
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2, 3, 5, 10, 11, 12, 17, 19, 20, 24, 27, 28, 29, 30, 33, 40, 42, 44, 59, 62, 65, 68, 70, 75, 82, 83, 93, 96, 101, 102, 107, 108, 109, 122, 123, 126, 132, 133, 134, 135, 136, 138, 142, 148, 149, 154, 155, 160, 165, 166, 167, 174, 178, 191, 195, 203, 205, 206
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OFFSET
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1,1
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COMMENTS
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The corresponding primes are 3, 7, 13, 31, 43, 71, 89, 109, 151,...
A property of this sequence : there are groups of consecutive numbers {2,3}, {10,11,12}, {19,20}, {27,28,29,30}, ... , {2707,2708,2709},..., most of which have length 2.
The lengths of these groups are 2, 3, 2, 4, 2, 2, 3, 2, 5, 2, 2, 3, 3, 5, 2, ... The first group of size 2, 3, 4, ... starts at n = 1, 4, 11, 37, 15034, 102941...
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LINKS
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EXAMPLE
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a(4) = 10 because sigma(a(1)) + sigma(a(2)) + sigma(a(3)) = sigma(2) + sigma(3) + sigma(5) = 3 + 4 + 6 = 13, and:
13 + sigma(6) = 13 + 12 = 25 is not prime,
13 + sigma(7) = 13 + 8 = 21 is not prime,
13 + sigma(8) = 13 + 15 = 28 is not prime, and
13 + sigma(9) = 13 + 13 = 26 is not prime, but
13 + sigma(10) = 13 + 18 = 31 is prime.
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MAPLE
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with(numtheory) :
option remember;
local a, p ;
if n = 1 then
2;
else
for a from procname(n-1)+1 do
p := add(sigma(procname(j)), j=1..n-1) + sigma(a) ;
if isprime(p) then
return a;
end if;
end do:
end if;
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MATHEMATICA
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seq = {}; s = 0; n = 0; Do[n++; While[!PrimeQ[(sd = s + DivisorSigma[1, n])], n++]; s = sd; AppendTo[seq, n], {100}]; seq (* Amiram Eldar, Sep 12 2019 *)
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CROSSREFS
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Cf. A000203 (sigma(n) = sum of divisors of n).
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KEYWORD
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nonn,less
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AUTHOR
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STATUS
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approved
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