A363513 a(1) = 2, then a(n) is the least prime p > a(n - 1) such that p + a(n-1) and p - a(n-1) have the same number of prime factors counted with multiplicity.

2, 5, 13, 31, 61, 103, 157, 173, 181, 193, 211, 223, 239, 269, 313, 337, 353, 419, 487, 499, 577, 613, 631, 647, 677, 709, 727, 827, 857, 947, 1039, 1093, 1117, 1231, 1283, 1303, 1319, 1483, 1499, 1553, 1609, 1627, 1657, 1693, 1721, 1733, 1823, 1913, 1933, 1951, 2003, 2027, 2039, 2129, 2161, 2203

Offset

1,1

Links

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

Formula

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

Example

a(2) = 5 because A001222(5-2) = A001222(5+2) = 1.
a(3) = 13 because A001222(13-5) = A001222(13+5) = 3.

Maple

R:= 2: r:= 2:
for i from 1 to 100 do
    p:= nextprime(r);
    while numtheory:-bigomega(r+p) <> numtheory:-bigomega(p-r) do
      p:= nextprime(p)
    od;
    R:= R, p; r:= p;
od:
R;

Mathematica

s = {p = 2}; Do[q = NextPrime[p]; While[PrimeOmega[p + q]
!= PrimeOmega[q - p], q = NextPrime[q]]; AppendTo[s, p = q], {200}]; s

Crossrefs

Cf. A001222, A361611.

Sequence in context: A077278 A073683 A098501 * A180302 A116701 A068739

Adjacent sequences: A363510 A363511 A363512 * A363514 A363515 A363516

Keyword

nonn

Author

Zak Seidov and Robert Israel, Jun 07 2023

Status

approved