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A219860 a(n) is the smallest number greater than a(n-1) such that sigma(a(1)) + sigma(a(2)) + ... + sigma(a(n)) is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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...
LINKS
EXAMPLE
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.
MAPLE
with(numtheory) :
A219860 := proc(n)
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;
end proc: # R. J. Mathar, Dec 19 2012
MATHEMATICA
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 *)
CROSSREFS
Cf. A000203 (sigma(n) = sum of divisors of n).
Sequence in context: A175481 A288244 A246392 * A076681 A047604 A104427
KEYWORD
nonn,less
AUTHOR
Michel Lagneau, Nov 29 2012
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)