login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115103 Primes p such that p-1 and p+1 have the same number of prime factors with multiplicity. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Adjacent sequences:  A115100 A115101 A115102 * A115104 A115105 A115106

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Mar 02 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)