A347170 The lexicographically earliest sequence with a(1) = 1 and Omega(a(i) + a(k)) = 3 for i < k <= n.

1, 7, 11, 91, 164, 931, 5131, 6403, 11811, 19507, 87907, 87914, 341811, 7961923, 7963880, 8037362, 8044275, 8140244, 8593387, 11055787, 14017267, 37262755, 164218555, 551667835, 2340626587, 2970952034, 3788070787

Offset

1,2

Comments

Sum of any two terms is in A014612. Is the sequence infinite?

Links

Table of n, a(n) for n=1..27.

Example

1 + 7 = 8 = A014612(1), 1 + 11 = 12 = A014612(2), 7 + 11 = 18 = A014612(3).

Mathematica

a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1] + 1}, While[! AllTrue[Array[a, n - 1], PrimeOmega[# + k] == 3 &], k++]; k]; Array[a, 12] (* Amiram Eldar, Sep 29 2021 *)

Prog

(PARI) first(n)=my(v=vector(n), t); v[1]=1; for(k=2, n, t=v[k-1]; while(t++, for(i=1, k-1, if(bigomega(v[i]+t)!=3, next(2))); break); v[k]=t); v; \\ Charles R Greathouse IV, Oct 03 2021
(PARI) nxt(v, n=v[#v]+1)=my(b=min(97, n-1)); while(1, for(i=1, #v, my(f=factor(v[i]+n, b), e=f[, 2]); if(vecsum(e)>3 || vecsum(e)==3 && !isprime(f[#e, 1]), n++; next(2))); for(i=1, #v, if(bigomega(v[i]+n)!=3, n++; next(2))); return(n)); \\ Charles R Greathouse IV, Oct 03 2021

Crossrefs

Cf. A001222 (Omega), A014612.

Sequence in context: A337099 A123763 A018680 * A107187 A132958 A371485

Adjacent sequences: A347167 A347168 A347169 * A347171 A347172 A347173

Keyword

nonn

Author

Zak Seidov, Sep 26 2021

Status

approved