A023524 -id:A023524 - cp's OEIS frontend

A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

0, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 2, 3, 2, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 4

Offset: 1

Clark Kimberling

nonn

This is taking prime(0)=1 (see first comment in A023515). - Vincenzo Librandi, Apr 27 2019

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A023515, A023524, A023568, A023575, A023582, A023589.

[#PrimeDivisors(NthPrime(n)*(NthPrime(n-1))-1): n in [1..100]]; // Vincenzo Librandi, Apr 27 2019

0,seq(nops(numtheory:-factorset(ithprime(n)*ithprime(n-1)-1)),n=2..120); # Muniru A Asiru, Apr 29 2019

Prepend[Table[PrimeNu[Prime[n] Prime[n-1] - 1], {n, 2, 80}],0] (* Vincenzo Librandi, Apr 27 2019 *)

a(n) = if (n==1, 0, omega(prime(n)*prime(n-1) - 1)); \\ Michel Marcus, Apr 30 2019

a(n) = A001221(A023515(n)).

A266163 Primes prime(k) such that (prime(k)*prime(k+1)+1)/2 is prime.

Original entry on oeis.org

467, 2179, 2777, 4877, 6151, 6173, 6871, 7907, 7937, 8329, 9791, 11261, 11287, 12119, 12227, 12941, 13009, 14657, 14831, 15061, 15607, 16127, 16193, 16453, 16787, 16831, 17989, 18701, 18803, 18947, 19507, 20483, 20521, 20627, 22291, 22397, 22409, 22877, 23497

Offset: 1

Robert Israel, Dec 22 2015

nonn

22397 and 22409 are first consecutive primes in this sequence. - Altug Alkan, Dec 22 2015

The next consecutive primes in this sequence are 134093 and 134129, 405541 and 405553, 432073 and 432097, 480803 and 480827, 586213 and 586237, ... - Harvey P. Dale, Dec 25 2015

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

Cf. A023524.

[p: p in PrimesInInterval(3,3*10^4) | IsPrime((p*NextPrime(p+1)+1) div 2)]; // Vincenzo Librandi, Dec 23 2015

lastp:= 3:
count:= 0:
while count < 100 do
  p:= nextprime(lastp);
  if isprime((lastp*p+1)/2) then
    count:= count+1;
    A[count]:= lastp;
  fi;
  lastp:= p;
od:
seq(A[i],i=1..100);

Prime@ Select[Range@ 2620, PrimeQ[(Prime@ # Prime[# + 1] + 1)/2] &] (* Michael De Vlieger, Dec 22 2015 *)
Transpose[Select[Partition[Prime[Range[50000]],2,1],PrimeQ[ (Times@@#+1)/2]&]] [[1]] (* Harvey P. Dale, Dec 25 2015 *)

lista(nn) = {forprime(p=3, nn, if(ispseudoprime((p*nextprime(p+1)+1)/2), print1(p, ", ")));} \\ Altug Alkan, Dec 22 2015

cp's OEIS Frontend

A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula