0,1

With an initial 1 added, this is the complement of the closure of {2} under a*b+1 and a*b-1. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 11 2006

Also the square root of the product of twin prime pairs + 1. Two consecutive odd numbers can be written as 2k+1,2k+3. Then (2k+1)(2k+3)+1 = 4(k^2+2k+1) = 4(k+1)^2, a perfect square. Since twin prime pairs are two consecutive odd numbers, the statement is true for all twin prime pairs. - Cino Hilliard (hillcino368(AT)gmail.com), May 03 2006

a(n) = A129297(n+2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 09 2007

Or, single (or isolated) composites. Also nonprimes k such that neither k-1 nor k+1 is nonprime. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 11 2009

Archimedeans Problems Drive, Eureka, 30 (1967).

T. D. Noe, Table of n, a(n) for n=0..10000

C. K. Caldwell, Twin Primes

C. K. Caldwell, Twin primes

Eric Weisstein's World of Mathematics, Twin Primes

Anonymous, Twin Prime Pairs from 3 to 10000000(actually expressed as a(n)-+1)

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

a(n) = {A001359(n+1) + A006512(n+1)}/2 = 2*A040040(n) = A054735(n+1)/2 = A111046(n+1)/4.

a(n) = A141515(n) iff A141515(n+1) -/+1 is both prime. [From Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Sep 19 2008]

ZL:=[]:for p from 1 to 1610 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL), (((p+2)^2)-p^2)/4]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2007

Select[Table[Prime[n] + 1, {n, 260}], PrimeQ[ # + 1] &] - Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 12 2005

Cf. A001359, A002822, A006512, A037074, A040040, A054735, A077800, A111046.

Sequence in context: A074998 A061715 A072570 this_sequence A034425 A073123 A079865

Adjacent sequences: A014571 A014572 A014573 this_sequence A014575 A014576 A014577

nonn,easy,nice

R. K. Guy, N. J. A. Sloane (njas(AT)research.att.com), Eric Weisstein (eric(AT)weisstein.com)