1,1

Also, solutions to phi(n + 2) = sigma(n). - Conjectured by Jud McCranie (j.mccranie(AT)comcast.net), Jan 03 2001; proved by Reinhard Zumkeller (REINHARD.ZUMKELLER(AT)LHSYSTEMS.COM), Dec 05 2002

Primes for which the weight as defined in A117078 is 3 gives this sequence except for the initial 3. - Remi Eismann (reismann(AT)free.fr), Feb 15 2007

The set of lesser of twin primes larger than three is a proper subset of the set of primes of the form 3n - 1 (A003627). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Jun 05 2008

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.

Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2.

A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

T. R. Nicely, Enumeration to 10^14 of the twin primes and Brun's constant, Virginia Journal of Science, 46:3 (Fall, 1995), 195-204.

C. K. Caldwell, Table of n, a(n) for n = 1..100000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

C. K. Caldwell, First 100000 Twin Primes

C. K. Caldwell, Twin Primes

C. K. Caldwell, Largest known twin primes

C. K. Caldwell, Twin primes

C. K. Caldwell, The prime pages

A. Granville and G. Martin, Prime number races

Thomas R. Nicely, Home page, which has extensive tables.

F. Richman, Generating primes by the sieve of Eratosthenes

P. Shiu, A Diophantine Property Associated with Prime Twins

T. Tao, Obstructions to uniformity, and arithmetic patterns in the primes

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for primes, gaps between

O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.

for i from 1 to 253 do if ithprime(i+1) = ithprime(i) + 2 then print({ithprime(i)}); fi; od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007

Select[ Prime[ Range[ 253]], PrimeQ[ # + 2] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2005)

Cf. A006512 (greater of twin primes), A014574, A001097, A077800.

a(n)=A077800(2n-1).

Cf. A002822, A040040, A054735, A067829, A082496, A088328.

Cf. A117078, A117563, A001359, A074822.

Cf. A003627.

Sequence in context: A063700 A078859 A054799 this_sequence A096292 A078864 A023218

Adjacent sequences: A001356 A001357 A001358 this_sequence A001360 A001361 A001362

nonn,nice,easy

njas