A208572 -id:A208572 - cp's OEIS frontend

A208574 Union of A208572 and A208573.

3, 5, 11, 17, 29, 41, 59, 71, 101, 137, 197, 269, 419, 521, 809, 1031, 1607, 2081, 3119, 4127, 6197, 8219, 12377, 16451, 24917, 32801, 49169, 65537, 98321, 131111, 196661, 262151, 393299, 524351, 786551, 1048889, 1572869, 2097257, 3145739, 4194581, 6292007

Offset: 1

Washington Bomfim, Feb 28 2012

nonn

Cf. A001359, A208572, A208573.

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

Original entry on oeis.org

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

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

nonn

			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).

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

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

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

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 *)

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

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

A212294 Sums of (zero or more) distinct twin primes.

Original entry on oeis.org

0, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Charles R Greathouse IV, Jun 21 2012

nonn

Assuming a Bertrand-like result for twin primes, that for every n > 3 there is a prime n < p < 2n such that either p-2 or p+2 is prime, the only missing terms are 1, 2, 4, 6, and 9.

Cf. A208572.

Conjecturally, a(n) = n+4 for n > 5. This holds at least up to 2^500.

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A208574 Union of A208572 and A208573.

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

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A212294 Sums of (zero or more) distinct twin primes.

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