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A274649 a(n) is the smallest odd prime that divides n + the sum of all smaller primes, or 0 if no such prime exists. 2
5, 3, 30915397, 11339869, 3, 5, 859, 3, 41, 233, 3, 7, 4175194313, 3, 307, 5, 3, 1459, 7, 3, 5, 9907, 3, 647, 13, 3, 31, 11, 3, 193, 5, 3, 7, 2939, 3, 5, 3167, 3, 11, 7, 3, 1321, 86629, 3, 17, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From David A. Corneth, Nov 12 2016 (Start):

a(n) is the smallest odd prime p such that p|(n + A007504(primepi(p) - 1)) or zero if p doesn't exist.

If a(n) = p then a(n + p) <= p. (End)

If n is congruent to 1 (mod 3), then a(n)=3.

a(2), a(3) and a(12) were found by Jack Brennen.

From Robert G. Wilson v, Nov 13 2016 (Start):

If n == 1 (mod 3) then a(n) = 3;

If n == 0 (mod 5) then a(n) = 5;

If n == 4 (mod 7) then a(n) = 7;

if n == 5 (mod 11) then a(n) = 11;

if n == 11 (mod 13) then a(n) = 13;

if n == 10 (mod 17) then a(n) = 17;

if n == 18 (mod 19) then a(n) = 19;

if n == 23 (mod 23) then a(n) = 23;

in that order, i.e.; from smaller to greater prime modulus, etc.

First occurrence of p>2: 1, 0, 11, 27, 24, 44, 56, 84, 161, ..., .

a(47) > 10^11.

(End).

LINKS

Table of n, a(n) for n=0..46.

Robert G. Wilson v, n and a(n) for n=0..10000 or 0 if no such value is known.

EXAMPLE

a(6) = 859 because 859 is the smallest odd prime that divides the sum of 6 + (sum of all primes smaller than itself).

a(8) = 41 because 8+2+3+5+7+11+13+17+!9+23+29+31+37+41 = 246 and 246/41 = 6.

MATHEMATICA

f[n_] := Block[{p = 3, s = n +2}, While[ Mod[s, p] != 0, s = s + p; p = NextPrime@ p]; p]; Array[f, 47, 0] (* Robert G. Wilson v, Nov 12 2016 *)

CROSSREFS

Cf. A007504, A007506, A024011, A274995.

Sequence in context: A304287 A121021 A237518 * A258234 A159799 A185579

Adjacent sequences:  A274646 A274647 A274648 * A274650 A274651 A274652

KEYWORD

nonn,more

AUTHOR

Neil Fernandez, Nov 10 2016

STATUS

approved

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Last modified November 14 00:06 EST 2018. Contains 317150 sequences. (Running on oeis4.)