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A173937
Smallest natural d = d(n) such that 2^n + d is lesser of twin primes (n = 0, 1, 2, ...).
6
2, 1, 1, 3, 1, 9, 7, 9, 13, 9, 7, 33, 31, 27, 67, 33, 1, 39, 7, 63, 313, 105, 277, 9, 73, 69, 457, 51, 121, 105, 7, 219, 91, 297, 247, 321, 115, 567, 1327, 411, 553, 987, 325, 183, 2065, 2565, 415, 879, 241, 459, 643, 1209, 391, 1155, 1477, 1449, 175, 129, 1045
OFFSET
0,1
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, New York, Springer-Verlag, 1994
Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, Berlin Heidelberg, 1996
Daniel Shanks, Solved and Unsolved Problems in Number Theory, 4th ed., New York, Chelsea, 1993
LINKS
Ken Takusagawa, Twin primes
EXAMPLE
2^0 + 2 = 3 = prime(2), 2^0 + 4 = 5 = prime(3).
2^1 + 1 = 3 = prime(2), 2^1 + 3 = 5 = prime(3).
2^2 + 1 = 5 = prime(3), 2^2 + 3 = 7 = prime(4).
MATHEMATICA
Join[{2}, Table[s = 2^n + 1; While[! (PrimeQ[s] && PrimeQ[s + 2]), s = s + 2]; s - 2^n, {n, 60}]] (* T. D. Noe, May 08 2012 *)
PROG
(PARI) A173937(n)={forstep(p=2^n\6*6+5, 2<<n, 6, isprime(p)||next; isprime(p+2)&return(p-2^n)); 2-n} \\ M. F. Hasler, Oct 21 2012
CROSSREFS
Cf. A001359, A006512, A208572 (smallest twin prime > 2^n).
Sequence in context: A003687 A104575 A318833 * A046223 A338398 A192181
KEYWORD
nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 03 2010
EXTENSIONS
Values a(0..300) double-checked by M. F. Hasler, Oct 21 2012
STATUS
approved