A067062 Numbers n such that sigma(n+2) - sigma(n) = prime(n+1) - prime(n).

3, 5, 17, 40, 41, 203, 1949, 2309, 2711, 2789, 2801, 3299, 3329, 3359, 3917, 4157, 4217, 4259, 4637, 5009, 5021, 5231, 6449, 6497, 7757, 8087, 8219, 8627, 9419, 9929, 10007, 10937, 11777, 12071, 14321, 15647, 15971, 16061, 16901, 18131, 18251

Offset

1,1

Comments

If n and n+2, prime(n) and prime(n+1) are twin primes, then n is in the sequence. But some values of n are composite.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Maple

with(numtheory); A067062:=n->`if`(sigma(n+2)-sigma(n)=ithprime(n+1)-ithprime(n), n, NULL); seq(A067062(n), n=1..20000); # Wesley Ivan Hurt, Nov 27 2013

Mathematica

okQ[n_]:=DivisorSigma[1, n+2]-DivisorSigma[1, n]==Prime[n+1]-Prime[n]; Select[Range[20000], okQ] (* Harvey P. Dale, May 24 2011 *)

Prog

(PARI) { default(primelimit, 4294965247); n=0; for (m=1, 10^10, if (sigma(m+2)-sigma(m) == prime(m+1)-prime(m), write("b067062.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, May 02 2010

Crossrefs

Sequence in context: A148518 A077796 A241249 * A148519 A148520 A148521

Adjacent sequences: A067059 A067060 A067061 * A067063 A067064 A067065

Keyword

nonn

Author

Benoit Cloitre, Feb 17 2002

Status

approved