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.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A219857 A219858 A219859 * A219861 A219862 A219863

Keyword

nonn,less

Author

Michel Lagneau, Nov 29 2012

Status

approved