A365145 Lexicographically least increasing sequence of triprimes (A014612) whose first differences are triprimes.

8, 20, 28, 70, 78, 98, 110, 130, 138, 165, 195, 207, 273, 285, 363, 426, 434, 442, 470, 498, 506, 518, 530, 548, 556, 574, 582, 590, 598, 606, 618, 638, 646, 654, 682, 710, 722, 730, 742, 754, 762, 782, 790, 834, 854, 874, 892, 942, 962, 970, 978, 986, 994, 1002, 1010, 1022, 1030, 1038, 1058

Offset

1,1

Comments

a(n) - a(n-1) >= 8. If a(n-1) = 4*p where p is in A001359 then a(n) - a(n-1) = 8.

Links

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

Example

a(2) = 20, a(3) = 28 = 2^2 * 7 is a triprime and 28 - 20 = 8 = 2^3 is a triprime, and this is the least number > 20 that works, so a(4) = 28.

Maple

R:= 8: m:= 8: count:= 1:
for t from 9 while count < 100 do
  if numtheory:-bigomega(t) = 3 and numtheory:-bigomega(t-m) = 3 then
    R:= R, t; m:= t; count:= count+1
  fi
od:
R;

Mathematica

Do[n = m + 8; While[{3, 3} != PrimeOmega[{n, n - m}],
n++]; AppendTo[s, m = n], {100}]; s

Crossrefs

Cf. A001359, A014612, A175588.

Sequence in context: A317760 A022757 A246308 * A194218 A339273 A017617

Adjacent sequences: A365142 A365143 A365144 * A365146 A365147 A365148

Keyword

nonn

Author

Zak Seidov and Robert Israel, Aug 23 2023

Status

approved