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

0,1

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

T. D. Noe, Table of n, a(n) for n = 0..300

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

Adjacent sequences: A173934 A173935 A173936 * A173938 A173939 A173940

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