OFFSET
1,1
COMMENTS
Either p-1 or p+1 must be of the form 2^i * 3^j, since among three consecutive numbers exactly one is a multiple of 3. - Giovanni Resta, Mar 29 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..51 (all terms < 10^75)
EXAMPLE
7 is not a term because n + 1 = 8 has only one prime factor.
23 is a term because it is prime and n - 1 = 22 has two distinct prime factors (2, 11) and n + 1 = 24 has two distinct prime factors (2, 3).
43 is not a term because n - 1 = 42 has three distinct prime factors (2, 3, 7).
MAPLE
N:= 10^20: # To get all terms <= N
Res:= {}:
for i from 1 to ilog2(N) do
for j from 1 to floor(log[3](N/2^i)) do
q:= 2^i*3^j;
if isprime(q-1) and nops(numtheory:-factorset((q-2)/2^padic:-ordp(q-2, 2)))=1 then Res:= Res union {q-1} fi;
if isprime(q+1) and nops(numtheory:-factorset((q+2)/2^padic:-ordp(q+2, 2)))=1 then Res:= Res union {q+1} fi
od od:
sort(convert(Res, list)); # Robert Israel, Apr 16 2017
MATHEMATICA
mx = 10^30; ok[t_] := PrimeQ[t] && PrimeNu[t-1]==2==PrimeNu[t+1]; Sort@ Reap[Do[ w = 2^i 3^j; Sow /@ Select[ w+ {1, -1}, ok], {i, Log2@ mx}, {j, 1, Log[3, mx/2^i]}]][[2, 1]] (* terms up to mx, Giovanni Resta, Mar 29 2017 *)
PROG
(Sage) omega=sloane.A001221; [n for n in prime_range(10^6) if 2==omega(n-1)==omega(n+1)]
(Sage) sorted([2^i*3^j+k for i in (1..40) for j in (1..20) for k in (-1, 1) if is_prime(2^i*3^j+k) and sloane.A001221(2^i*3^j+2*k)==2])
(PARI) isok(n) = isprime(n) && (omega(n-1)==2) && (omega(n+1)==2); \\ Michel Marcus, Apr 17 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Giuseppe Coppoletta, Mar 28 2017
EXTENSIONS
a(33)-a(34) from Giovanni Resta, Mar 29 2017
STATUS
approved