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A128926
Smaller member p of a pair of consecutive primes (p,q) such that either q^2-p^2+1 or q^2-p^2-1 is also prime.
0
3, 5, 7, 11, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 73, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 281, 307, 311, 313, 331, 337, 353, 359, 367, 373, 379
OFFSET
1,1
EXAMPLE
3 and 5 are consecutive primes, 5^2-3^2 = 25-9 = 16. 17 is prime, hence 3 is in the sequence.
79 and 83 are consecutive primes, 83^2-79^2 = 6889-6241 = 648. 647 is prime, hence 79 is in the sequence.
89 and 97 are consecutive primes, 97^2-89^2 = 9409-7921 = 1488. 1487 (as well as 1489) is prime, hence 89 is in the sequence.
MAPLE
isA128926 := proc(n) local p, q ; p := ithprime(n) ; q := ithprime(n+1) ; isprime((p+q)*(q-p)+1) or isprime((p+q)*(q-p)-1) ; end:
for n from 1 to 100 do if isA128926(n) then printf("%d, ", ithprime(n)) ; fi ; od ; # R. J. Mathar, Apr 26 2007
MATHEMATICA
Prime@ Select[ Range@ 75, PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 - 1] || PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 + 1] &] (* Robert G. Wilson v *)
PROG
(Magma) [ p: p in PrimesUpTo(380) | IsPrime(q^2-p^2-1) or IsPrime(q^2-p^2+1) where q is NextPrime(p) ]; /* Klaus Brockhaus, May 05 2007 */
CROSSREFS
Cf. A069482.
Sequence in context: A225223 A346794 A226653 * A139559 A158361 A342692
KEYWORD
nonn
AUTHOR
J. M. Bergot, Apr 25 2007
EXTENSIONS
Corrected and extended by Robert G. Wilson v, R. J. Mathar and Klaus Brockhaus, Apr 26 2007
STATUS
approved