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A115103
Primes p such that p-1 and p+1 have the same number of prime factors with multiplicity.
6
5, 19, 29, 43, 67, 89, 151, 173, 197, 233, 271, 283, 307, 317, 349, 461, 491, 569, 571, 593, 653, 701, 739, 751, 787, 857, 859, 907, 919, 1013, 1061, 1097, 1277, 1291, 1303, 1483, 1667, 1747, 1831, 1867, 1889, 1913, 1973, 2003, 2083, 2131, 2311, 2357, 2393
OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
EXAMPLE
19-1 = 2*3*3 has 3 factors. 19+1 = 2*2*5 has 3 factors. So 19 is in the table.
MAPLE
isA115103 := proc(n)
if not type(n, prime) then
return false;
end if;
if numtheory[bigomega](n-1) <> numtheory[bigomega](n+1) then
false;
else
true ;
end if ;
end proc:
for n from 2 to 3000 do
if isA115103(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Feb 13 2019
# second Maple program:
q:= p-> isprime(p) and (f-> f(p+1)=f(p-1))(numtheory[bigomega]):
select(q, [$1..3000])[]; # Alois P. Heinz, May 08 2022
MATHEMATICA
Select[Prime[Range[400]], PrimeOmega[#-1]==PrimeOmega[#+1]&] (* Harvey P. Dale, Apr 26 2014 *)
PROG
(PARI) g(n) = forprime(x=1, n, p1=bigomega(x-1); p2=bigomega(x+1); if(p1==p2, print1(x", ")))
CROSSREFS
Cf. A067386 (without multiplicity), A323498, A323536, A323537.
Sequence in context: A341079 A045456 A115167 * A241043 A045457 A165557
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Mar 02 2006
STATUS
approved