A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k).

7, 12, 14, 18, 22, 38, 58, 158, 178, 382, 502, 542, 718, 878, 1202, 1318, 1382, 1438, 1622, 1822, 2018, 2558, 2578, 2858, 2902, 3062, 3118, 3778, 4282, 4358, 4442, 4678, 4702, 5078, 5098, 5582, 5638, 5702, 5938, 6338, 6638, 6662, 6718, 6998, 7418, 8222, 8782, 8818, 9182, 9662, 9902

Offset: 1

Author

Kevin D. Woerner, Aug 03 2018

Keywords

• nonn

Comments

Besides the 1st, 2nd, and 4th terms, a(n) is 2 times a prime, one of a(n)-1 or a(n)+1 is a prime, and the other number is 3 times a prime.

The 10 in the definition is the smallest value for which this is a possibly infinite list.

Examples

			For a(3)=14, sigma_0(13)=2, sigma_0(14)=4, and sigma_0(15)=4, hence sigma_0(a(3)-1) + sigma_0(a(3)) + sigma_0(a(3)+1) = 10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005.

Programs

Maple

Res:= 7,12,14,18: count:= 4:
p:= 9:
while count < 100 do
  p:= nextprime(p);
  n:= 2*p;
  if n mod 3 = 1 then v:= isprime(n+1) and isprime((n-1)/3)
  else v:= isprime(n-1) and isprime((n+1)/3)
  fi;
  if v then count:= count+1; Res:= Res, n fi
od:
Res; # Robert Israel, Aug 27 2018

Mathematica

Select[Partition[Range[10^4], 3, 1], Total@ DivisorSigma[0, #] == 10 &][[All, 2]] (* Michael De Vlieger, Aug 05 2018 *)

PARI

isok(n) = numdiv(n-1) + numdiv(n) + numdiv(n+1) == 10; \\ Michel Marcus, Aug 04 2018