A120640 Primes such that their quadruple is not 1 away from a prime number.

19, 23, 29, 31, 47, 59, 61, 89, 101, 103, 107, 109, 113, 149, 151, 157, 167, 179, 181, 191, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 283, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 379, 389, 397, 401, 419, 421, 439, 443, 449, 457, 461, 463

Offset

1,1

Comments

This sequence is a variation of the sequence in the reference. However, this sequence should have an infinite number of terms. k=4 in the PARI code.

References

R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.18.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Example

19*4 = 76, which is one away from 75 and 77 both not prime.

Mathematica

Select[Prime[Range[100]], AllTrue[4#+{1, -1}, CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 09 2015 *)

Prog

(PARI) primepm3(n, k) = =number of iterations, k = factor { local(x, p1, p2, f1, f2, r); if(k%2, r=2, r=1); for(x=1, n, p1=prime(x); p2=prime(x+1); if(!isprime(p1*k+r)&!isprime(p1*k-r), print1(p1", ") ) ) }

Crossrefs

Sequence in context: A073319 A274048 A334093 * A309360 A151768 A270083

Adjacent sequences: A120637 A120638 A120639 * A120641 A120642 A120643

Keyword

easy,nonn

Author

Cino Hilliard, Aug 17 2006

Status

approved