The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A214150 Least prime p such that the factorization of p^2 - 25 contains n consecutive primes beginning with prime(4)=7. 2
19, 61, 863, 5231, 84859, 532537, 3432203, 255634241, 4594884299, 44139608287, 644772297031, 33055909092211, 271103095974079, 93380069969929969, 1151842860713446127, 22664072571698543617, 2801339281067798957117, 137197247292115717439959 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
p^2 - 25 does contain the prime factors 2, 3, but not 5: p - 5 and p + 5 are not divisible by 5 and p^2 - 25 is divisible by 24 as primes are 1 or 2 mod 3 and thus p - 5 or p + 5 are 0 mod 3 and primes are 1 or 3 mod 4 and thus p - 5 or p + 5 are 0 mod 4 and both p - 5 and p + 5 are even.
In general, if p > k is prime and k is odd and not divisible by 3, p^2 - k^2 is divisible by 24.
LINKS
EXAMPLE
a(4) = 5231, 5226 = 2*3*13*67, 5236 = 2^2*7*11*17, the factorization of 5231^2 - 25 contains the 4 consecutive primes 7, 11, 13 and 17 beginning with 7.
PROG
(PARI) A214150(n)=
{ local(a, k=1, p);
a=prod(j=4, n+3, prime(j));
while( 1,
if( issquare(24*k*a+25, &p),
if( ispseudoprime(p), return(p) )
);
k++;
)}
(Python)
from itertools import product
from sympy import isprime, sieve, prime
from sympy.ntheory.modular import crt
def A214150(n): return 19 if n == 1 else int(min(filter(lambda n: n > 5 and isprime(n), (crt(tuple(sieve.primerange(7, prime(n+3)+1)), t)[0] for t in product((5, -5), repeat=n))))) # Chai Wah Wu, Jun 01 2022
CROSSREFS
Sequence in context: A341081 A201812 A262317 * A262920 A183455 A183340
KEYWORD
nonn
AUTHOR
Robin Garcia, Jul 05 2012
EXTENSIONS
More terms from Max Alekseyev, Aug 22 2012
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 May 19 09:42 EDT 2024. Contains 372683 sequences. (Running on oeis4.)