A357713 -id:A357713 - cp's OEIS frontend

A364442 a(n) is the smallest number > a(n-1) such that a(n-1) + a(n) is a triprime (A014612), with a(1) = 1.

1, 7, 11, 16, 26, 37, 38, 40, 52, 53, 57, 59, 65, 73, 74, 79, 85, 86, 88, 94, 96, 99, 108, 114, 116, 120, 122, 123, 132, 134, 139, 140, 142, 143, 147, 163, 169, 174, 180, 183, 186, 188, 197, 202, 204, 206, 212, 213, 215, 219, 223, 229, 236, 238, 239, 244, 250, 256, 262, 268, 271, 277, 278, 283

Offset: 1

Zak Seidov and Robert Israel, Jul 25 2023

nonn

For n > 1, a(n) is the least number > a(n-1) such that A001222(a(n) + a(n-1)) = 3.

a(n-1) + a(n) is the least triprime > 2*a(n-1).

			a(3) = 11 because a(2) = 7, none of 7 + 8 = 15, 7 + 9 = 16 and 7 + 10 = 17 is a triprime, but 7 + 11 = 18 = 2*3^2 is a triprime.

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

Cf. A001222, A014612, A073627, A263349, A357713.

R:= 1: x:= 1:
for i from 1 to 100 do
   for y from x+1 while numtheory:-bigomega(x+y) <> 3 do od:
   R:= R,y;
   x:= y
od:
R;

s = {p = 1}; Do[q = p + 1; While[3 != PrimeOmega[p + q],
q++];  AppendTo[s, p = q], {100}]; s

A363786 a(0) = 2. For n >= 1, a(n) is the least prime p such that a(n-1) + p has n prime factors counted with multiplicity.

Original entry on oeis.org

2, 3, 3, 5, 11, 37, 59, 229, 347, 421, 3163, 4517, 1627, 26021, 14939, 34213, 64091, 378277, 14939, 3392933, 146011, 6931877, 8796763, 37340581, 25573979, 238667173, 113654363, 1018807717, 491141723, 4743349669, 8544205403, 10246276517, 491141723

Offset: 0

Zak Seidov and Robert Israel, Jun 21 2023

nonn

			a(5) = 37 because a(4) + 37 = 48 = 2^4*3 has 5 prime factors counted with multiplicity.

Cf. A001222, A357713.

R:= 2: t:= 2:
for n from 1 to 30 do
  p:= 1:
  do p:= nextprime(p)
  until numtheory:-bigomega(t+p) = n;
  R:= R,p;
  t:= p;
od:
R;

s={2};Do[p=2;While[PrimeOmega[s[[-1]]+p]!=
k,p=NextPrime[p]];Print[p];AppendTo[s,p],{k,1,50}];

A001222(a(n-1) + a(n)) = n.

cp's OEIS Frontend

A364442 a(n) is the smallest number > a(n-1) such that a(n-1) + a(n) is a triprime (A014612), with a(1) = 1.

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