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A361796
Prime numbers preceded by two consecutive numbers which are products of four distinct primes (or tetraprimes).
1
8647, 15107, 20407, 20771, 21491, 23003, 23531, 24767, 24971, 27967, 29147, 33287, 34847, 36779, 42187, 42407, 42667, 43331, 43991, 46807, 46867, 51431, 52691, 52747, 53891, 54167, 58567, 63247, 63367, 69379, 71711, 73607, 73867, 74167, 76507, 76631, 76847, 80447, 83591, 84247, 86243
OFFSET
1,1
EXAMPLE
8647 (prime), 8646 = 2*3*11*131 and 8645 = 5*7*13*19.
15107 (prime), 15106 = 2*7*13*83 and 15105 = 3*5*19*53.
20407 (prime), 20406 = 2*3*19*179 and 20405 = 5*7*11*53.
MAPLE
N:= 10^5: # for terms <= N
TP:= NULL:
P:= select(isprime, [2, seq(i, i=3..N/30, 2)]):
for i from 1 to nops(P) do
for j from 1 to i-1 while P[i]*P[j] <= N/6 do
for k from 1 to j-1 while P[i]*P[j]*P[k] <= N/2 do
TP:= TP, op(select(`<=`, map(`*`, P[1..k-1], P[i]*P[j]*P[k]), N));
od od od:
TP:= {TP}:
TTP:= TP intersect map(`-`, TP, 1):
sort(convert(select(isprime, map(`+`, TTP, 2)), list)); # Robert Israel, Apr 28 2023
MATHEMATICA
q[n_] := FactorInteger[n][[;; , 2]] == {1, 1, 1, 1}; Select[Prime[Range[10^4]], AllTrue[# - {1, 2}, q] &] (* Amiram Eldar, Apr 26 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Apr 26 2023
STATUS
approved