A364776 Lexicographically least increasing sequence of triprimes whose first differences are semiprimes.

8, 12, 18, 27, 42, 52, 66, 70, 76, 98, 102, 116, 125, 147, 153, 174, 188, 222, 231, 245, 255, 261, 275, 279, 285, 310, 316, 322, 332, 338, 363, 369, 402, 406, 410, 425, 429, 435, 470, 474, 483, 498, 507, 556, 578, 582, 596, 602, 606, 610, 645, 651, 657, 663, 678, 682, 692, 725, 747, 762, 772, 782

Offset

1,1

Comments

For n >= 2, a(n) is the least member k of A014612 such that k - a(n-1) is in A001358.

Links

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

Example

a(4) = 27 because a(3) = 18, 27 = 3^3 is a triprime, and 27 - 18 = 9 = 3^2 is a semiprime.

Maple

R:= 8: count:= 1: x:= 8:
for i from 9 while count < 100 do
  if numtheory:-bigomega(i) = 3 and numtheory:-bigomega(i-x) = 2 then
    R:= R, i; count:= count+1; x:= i;
  fi
od:
R;

Mathematica

s = {8, 12, 18, m=27}; Do[n = m + 4; While[3 != PrimeOmega[n] || 2
!= PrimeOmega[n - m], n++]; AppendTo[s, m = n], {100}]; s

Crossrefs

Cf. A001358, A014612.

Sequence in context: A171241 A120137 A274951 * A379033 A033477 A105936

Adjacent sequences: A364773 A364774 A364775 * A364777 A364778 A364779

Keyword

nonn

Author

Zak Seidov and Robert Israel, Aug 06 2023

Status

approved