A361073 Lexicographically least increasing sequence of triprimes (A014612) a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also triprimes.

8, 20, 50, 125, 279, 426, 531, 539, 814, 822, 897, 1002, 1010, 1076, 1146, 1209, 1325, 1353, 1398, 1406, 1516, 1558, 1868, 1898, 1948, 1978, 1986, 2013, 2225, 2233, 2397, 2527, 2547, 2575, 2763, 2783, 2810, 2908, 2938, 2946, 3009, 3054, 3081, 3414, 3422, 3452, 3522, 3567, 3714, 3759, 3786, 3813

Offset

1,1

Links

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

Example

a(3) = 50 because 50 = 2^2*5, 50 - a(2) = 30 = 2*3*5 and 50 + a(2) = 70 = 2*5*7 are all products of 3 (not necessarily distinct) primes, and 50 is the least number that works.

Maple

A[1]:= 8:
for i from 2 to 100 do
  for x from A[i-1]+8 do
    if numtheory:-bigomega(x) = 3 and numtheory:-bigomega(x-A[i-1]) = 3 and numtheory:-bigomega(x+A[i-1]) = 3 then
       A[i]:= x; break
    fi
od od:
seq(A[i], i=1..100);

Mathematica

s = {m = 8}; Do[p = m + 8; While[{3, 3, 3} != PrimeOmega[{p, m + p,
p - m}], p++];  AppendTo[s, m = p], {50}]; s

Crossrefs

Cf. A014612, A361611, A361215.

Sequence in context: A273304 A169878 A107816 * A361215 A205219 A232401

Adjacent sequences: A361070 A361071 A361072 * A361074 A361075 A361076

Keyword

nonn

Author

Zak Seidov and Robert Israel, Apr 09 2023

Status

approved