A264834 Integers k such that A008347(k) is divisible by k.

1, 19, 27, 1293, 41419, 41493, 41519, 41521, 41601, 1629899, 3142492081, 3142492231

Offset: 1

Author

Altug Alkan, Nov 26 2015

Keywords

• nonn
• more

Comments

Inspired by A008347.

a(n) - a(n-1) = 2 for n = 8.

a(11) > 10^9. - David A. Corneth, Aug 29 2018

a(13) > 7.35*10^12, if it exists. - Giovanni Resta, Sep 05 2018

Examples

			For first 19 prime numbers, (2 - 3 + 5 - 7 + 11 - 13 + 17 - 19 + 23 - 29 + 31 - 37 + 41 - 43 + 47 - 53 + 59 - 61 + 67) mod 19 = 38 mod 19 = 0. So a(2) = 19.
		

Links

• Romeo Meštrović, On the distribution of primes in the alternating sums of concecutive primes [sic], arXiv:1805.11657 [math.NT], 2018.

Crossrefs

Cf. A008347.

Programs

Mathematica

Select[Range@ 1500, Mod[Abs@ Sum[(-1)^k Prime[# - k], {k, 0, # - 1}], #] == 0 &] (* Michael De Vlieger, Nov 27 2015, after Robert G. Wilson v at A008347 *)

PARI

for(n=1, 1e5, if(sum(k=0, n-1, (-1)^(k)*prime(n-k)) % n == 0, print1(n,", ")))

PARI

upto(n) = my(s = t = 0, u=prime(n), res=List()); forprime(p=2, u, t++; s = (p - s); if(s % t == 0, listput(res, i))); res \\ David A. Corneth, Aug 29 2018

Formula

a(n) mod 2 = 1.

Extensions

a(10) from David A. Corneth, Aug 29 2018

a(11)-a(12) from Giovanni Resta, Sep 03 2018