

A063983


Least k such that k*2^n +/ 1 are twin primes.


20



4, 2, 1, 9, 12, 6, 3, 9, 57, 30, 15, 99, 165, 90, 45, 24, 12, 6, 3, 69, 132, 66, 33, 486, 243, 324, 162, 81, 90, 45, 345, 681, 585, 375, 267, 426, 213, 429, 288, 144, 72, 36, 18, 9, 147, 810, 405, 354, 177, 1854, 927, 1125, 1197, 666, 333, 519, 1032, 516, 258, 129, 72
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OFFSET

0,1


COMMENTS

Excluding the first three terms, all remaining terms have digital root 3, 6, or 9.  J. W. Helkenberg, Jul 24 2013


REFERENCES

Richard Crandall and Carl Pomerance, 'Prime Numbers: A Computational Perspective,' SpringerVerlag, NY, 2001, page 12.


LINKS



EXAMPLE

a(3) = 9 because 9*2^3=72 and 71 and 73 are twin primes.
n=6: a(6)=3, 64.3=192 and {191,193} are both primes; n=71: a(71)=630, 630*[2^71]=1487545442103938242314240 and {1487545442103938242314239, 1487545442103938242314241} are twin primes.


MATHEMATICA

Table[Do[s=(2^j)*k; If[PrimeQ[s1]&&PrimeQ[s+1], Print[{j, k]], {k, 1, 2*j^2], {j, 0, 100]; (*outprint of a[j]=k*)
Do[ k = 1; While[ ! PrimeQ[ k*2^n + 1 ]  ! PrimeQ[ k*2^n  1 ], k++ ]; Print[ k ], {n, 0, 50} ]
f[n_] := Block[{k = 1}, While[Nand @@ PrimeQ[{1, 1} + 2^n*k], k++ ]; k]; Table[f[n], {n, 60}] (* Ray Chandler, Jan 09 2009 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



