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A192297 Lesser of pseudo twin primes to base 2. 2
561, 643, 645, 1103, 1905, 2465, 2699, 2819, 4369, 4371, 4679, 6599, 10259, 12799, 14489, 16703, 18719, 19949, 23001, 25759, 25761, 29339, 30119, 31607, 33151, 39863, 41039, 42797, 49139, 52631, 55243, 60701, 62743, 68099, 72883, 83663, 85487, 87249, 90749 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We call numbers {n,n+2} pseudo twin primes to base 2 if at least one of them is composite, while 2^(n-1)==1 (mod n) and 2^(n+1)==1 mod (n+2).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

2^(a(n)+2) == 3*a(n)+8 (mod a(n)*(a(n)+2)).

MAPLE

a:= proc(n) option remember; local k;

      for k from 2+`if` (n=1, 1, a(n-1)) by 2 while

        isprime(k) and isprime(k+2) or

          (2&^(k-1) mod k)<>1 or (2&^(k+1) mod (k+2))<>1

      do od; k

    end:

seq (a(n), n=1..40);  # Alois P. Heinz, Oct 13 2011

MATHEMATICA

fQ[n_] := (! PrimeQ[n] || ! PrimeQ[n + 2]) && PowerMod[2, n - 1, n] == 1 && PowerMod[2, n + 1, n + 2] == 1; Select[2 Range@ 32000 + 1, fQ] (* Robert G. Wilson v, Oct 11 2011 *)

PROG

(PARI) is(n)=Mod(2, n^2+2*n)^(n+2)==3*n+8 && (!isprime(n) || !isprime(n+2)) && n>1 \\ Charles R Greathouse IV, Dec 02 2014

CROSSREFS

Cf. A001567, A002997, A141232.

Sequence in context: A344673 A344706 A259172 * A080747 A306487 A074380

Adjacent sequences:  A192294 A192295 A192296 * A192298 A192299 A192300

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Oct 11 2011

STATUS

approved

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Last modified October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)