A370575 Least increasing sequence of semiprimes with alternating parity such that a(n) - a(n-1) is a semiprime, with a(1) = 4.

4, 25, 34, 49, 58, 91, 106, 115, 166, 187, 202, 217, 226, 235, 274, 289, 298, 319, 334, 355, 394, 403, 454, 469, 478, 493, 502, 511, 526, 535, 586, 611, 626, 635, 674, 689, 698, 707, 746, 755, 794, 803, 818, 843, 878, 893, 914, 923, 958, 973, 982, 1003, 1018, 1027, 1042, 1057, 1082, 1115, 1154

Offset

1,1

Links

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

Example

a(3) = 34 because 34 = 2 * 17 is the first even semiprime > a(2) = 25.

Maple

N:= 100: # for a(1) .. a(N)
V:= Vector(N): V[1]:= 4: x:= 4:
for i from 2 to N do
  for y from x+1 by 2 do
    if numtheory:-bigomega(y) = 2 and numtheory:-bigomega(y-x) = 2 then
       x:= y; V[i]:= y; break
    fi
od od:
convert(V, list);

Mathematica

s={4}; Do[k = s[[-1]] + 1; While[{2, 2} != PrimeOmega[ {k, k - s[[-1]]}], k = k + 2]; AppendTo[s, k], {30}]; s

Crossrefs

Cf. A001358, A254923, A364679.

Sequence in context: A302416 A303183 A175052 * A240164 A169600 A267765

Adjacent sequences: A370572 A370573 A370574 * A370576 A370577 A370578

Keyword

nonn

Author

Zak Seidov and Robert Israel, Feb 22 2024

Status

approved