A173937 Smallest natural d = d(n) such that 2^n + d is lesser of twin primes (n = 0, 1, 2, ...).

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

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 03 2010

Keywords

• nonn

Examples

			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).
		

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

• Robert G. Wilson v, Table of n, a(n) for n = 0..3000 (0..300 from T. D. Noe).
• Ken Takusagawa, Twin primes

Crossrefs

Cf. A001359, A006512, A124001, A208572 (smallest twin prime > 2^n).

Programs

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 *)

PARI

A173937(n)={forstep(p=2^n\6*6+5,2<M. F. Hasler, Oct 21 2012

Extensions

Values a(0..300) double-checked by M. F. Hasler, Oct 21 2012