A361073 -id:A361073 - cp's OEIS frontend

A361215 Intersection of A361073 and 2 * A361611.

8, 20, 50, 1406, 1516, 1558, 1868, 1898, 1948, 1978, 1986, 5862, 5972, 6014, 7122, 7966, 7996, 8270, 8348, 8366, 8548, 8618, 21092, 31804, 31822, 32158, 33092, 33162, 33316, 33414, 37124, 37190, 37292, 37394, 39164, 39214, 39316, 39346, 39484, 39562, 39604, 39622, 39692, 39794, 45044, 45244

Offset: 1

Zak Seidov and Robert Israel, Apr 09 2023

nonn

If A361073(j) = 2*A361611(k) then x = 2*A361611(k+1) has the property that x, x - A361073(j) and x + A361073(j) are triprimes, so x >= A361073(j+1), with equality if and only if A361073(j+1) is even.

			a(4) = 1406 is a term because 1406 = A361073(20) = 2*A361611(17).

Robert Israel, Table of n, a(n) for n = 1..2900

Cf. A361073, A361611.

A:= {8}: lasta:= 8:
for i from 2 to 1000 do
  for x from lasta+8 do
    if numtheory:-bigomega(x) = 3 and numtheory:-bigomega(x-lasta) = 3 and numtheory:-bigomega(x+lasta) = 3 then
       A:= A union {x}; lasta:= x; break
    fi
od od:
R:= {8}: lastb:= 4:
while 2*lastb < lasta do
for x from lastb+4 do
  if numtheory:-bigomega(x) = 2 and numtheory:-bigomega(x-lastb) = 2 and numtheory:-bigomega(x+lastb) = 2 then
     if member(2*x,A) then R:= R union {2*x} fi;
     lastb:= x; break
  fi
od od:
sort(convert(R,list));

A368078 Lexicographically earliest increasing sequence a(n) of products of 4 primes such that a(n) - a(n-1) and a(n) + a(n-1) are also products of 4 primes. The 4 primes are counted with multiplicity.

Original entry on oeis.org

16, 40, 100, 250, 558, 852, 1062, 1078, 1628, 1644, 1794, 2004, 2020, 2152, 2292, 2418, 2650, 2706, 2796, 2812, 3032, 3116, 3736, 3796, 3896, 3956, 3972, 4026, 4450, 4466, 4794, 5054, 5094, 5150, 5525, 5661, 5697, 5925, 6201, 6225, 6325, 6550, 6566, 6606, 6756, 6856, 6956, 7016, 7076, 8030, 8214

Offset: 1

Zak Seidov and Robert Israel, Dec 11 2023

nonn

a(n) is the least number k > a(n-1) such that k, k - a(n-1), and k + a(n-1) are all in A014613.

			a(3) = 100 because a(2) = 40 and 100 = 2^2 * 5^2, 100 - 40 = 60 = 2^2 * 3 * 5 and 100 + 40 = 140 = 2^2 * 4 * 7 are all in A014613.

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

Cf. A014613, A361073.

isA014613:= proc(n) option remember; numtheory:-bigomega(n) = 4 end proc:
R:= 16: a:= 16: count:= 1:
while count < 100 do
  for x from a+16 do
    if isA014613(x-a) and isA014613(x) and isA014613(x+a) then break fi
  od;
  R:= R,x; a:= x; count:= count+1;
od:
R;

s = {m = 16}; Do[p = m + 16; While[{4, 4, 4} != PrimeOmega[{p, m +
p, p - m}], p++]; AppendTo[s, m = p], {50}]; s

cp's OEIS Frontend

A361215 Intersection of A361073 and 2 * A361611.

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