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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..57.

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: A085498 A225223 A226653 * A139559 A158361 A048184

Adjacent sequences:  A128923 A128924 A128925 * A128927 A128928 A128929

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

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Last modified March 7 14:00 EST 2021. Contains 341886 sequences. (Running on oeis4.)