A361490 a(1) = 8; for n > 1, a(n) is the least triprime > a(n-1) such that a(n) - a(n-1) and a(n) + a(n-1) are both prime.

8, 45, 52, 75, 92, 99, 130, 147, 164, 195, 236, 255, 266, 333, 406, 423, 430, 477, 494, 555, 574, 627, 670, 711, 716, 777, 782, 801, 806, 903, 908, 915, 932, 935, 938, 969, 1010, 1017, 1022, 1065, 1076, 1233, 1244, 1443, 1474, 1479, 1490, 1533, 1556, 1635, 1724, 1737, 1790, 1833, 1844, 2007, 2012

Offset

1,1

Comments

a(n) == n-1 (mod 2).

Links

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

Example

a(4) = 75 because 75 = 3*5^2 is a triprime > a(3) = 52, 75 - 52 = 23 and 75 + 52 = 127 are prime, and none of the earlier triprimes > 52 (63, 66, 68, 70) works.

Maple

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

Mathematica

s={8}; m=8; Do[n = m + 1; While[3 != PrimeOmega[n] || ! PrimeQ[m + n] || ! PrimeQ[n - m], n++]; Print[m=n]; AppendTo[s, m], {10}]

Crossrefs

Cf. A014612.

Sequence in context: A174643 A181268 A374281 * A075863 A118838 A153828

Adjacent sequences: A361487 A361488 A361489 * A361491 A361492 A361493

Keyword

nonn

Author

Zak Seidov and Robert Israel, Mar 14 2023

Status

approved