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A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A000005.

Sequence in context: A173417 A031021 A153245 * A062730 A287562 A073255

Adjacent sequences:  A317667 A317668 A317669 * A317671 A317672 A317673

KEYWORD

nonn

AUTHOR

Kevin D. Woerner, Aug 03 2018

STATUS

approved

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Last modified May 18 09:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)