A065749 -id:A065749

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A065750

Smaller term of a pair of twin primes of form (prime(i) - i)*(prime(i) + i) +- 1; the i is from A065749.

+20
2

239, 4127, 6359, 76367, 204599, 715679, 819911, 1333991, 2189879, 2394479, 6358271, 6571151, 7493879, 12968687, 13871591, 17450159, 31072007, 33552359, 33642839, 36950759, 46023119, 67300991, 81589967, 97950287, 105652007

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

OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = (A000040(A065749(n)) - A065749(n))*(A000040(A065749(n)) + A065749(n)) - 1. [corrected by Harry J. Smith, Oct 30 2009]

EXAMPLE

6359 = a(3) and 6361 is a twin prime: a(3) = (A000040(A065749(3)) - A065749(3))*(A000040(A065749(3)) + A065749(3)) - 1 = (A000040(23) - 23)*(A000040(23) -23) - 1 = (83 - 23)*(83 + 23) - 1 = 106*60 - 1 = 6360 - 1 = 6359. [corrected by Harry J. Smith, Oct 30 2009]

PROG

(PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, b=(prime(m) - m) * (prime(m) + m); if (isprime(b - 1) && isprime(b + 1), write("b065750.txt", n++, " ", b - 1); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 30 2009

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 21 2001

EXTENSIONS

More terms from Naohiro Nomoto, Nov 29 2001

Offset changed from 0 to 1 by Harry J. Smith, Oct 30 2009

STATUS

approved

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