A050200 @ A034961

[Robert G. Wilson v]

Neil,

	Just added the Mathematica coding and changed the offset from 0 to 1. In
this sequence vs. A050200 I find that only 17.6528% are congruent (mod 3) in
the first million terms. But the percentage is not stable. That is when I asked
for 10^n, I got: 1, 9, 119, 1463, 16401, 176528.

Thanx, Bob.



%I A034961
%S A034961 10,15,23,31,41,49,59,71,83,97,109,121,131,143,159,173,187,199,211,223,
%T A034961 235,251,269,287,301,311,319,329,349,371,395,407,425,439,457,471,487,
%U A034961 503,519,533,551,565,581,589,607,633,661,679,689,701,713,731,749,771
%N A034961 Sums of three consecutive primes.
%e A034961 E.g. 565 = 181 + 191 + 197.
%t A034961 Plus @@@ Partition[ Prime[ Range[60]], 3, 1] (from RGWv Feb 11 2005)
%Y A034961 Cf. A001043, A011974, A034707.
%K A034961 nonn
%O A034961 0,1
%A A034961 Patrick De Geest (pdg(AT)worldofnumbers.com), Oct 15 1998.


Neil,

	I see how we got this sequence. It is not the "Sum of three consecutive
primes." The coding is incorrect. I have created the same coding in
Mathematica. What the program does is first find the n_th prime number, p. Then
find the next prime number after p+1 and the next prime number after p+3. The
problem arises because p+2 is not necessarily a prime.

	Here is a stab at a correct title. "Beginning with p, a prime number, add to it 
the next prime numbers after p+1 and p+3."

Thanx, Bob.



%I A050200
%S A050200 10,15,23,29,41,47,59,65,81,97,105,119,131,137,153,171,187,195,209,223,
%T A050200 231,245,261,283,299,311,317,329,335,367,389,405,425,437,457,465,483,
%U A050200 497,513,531,551,563,581,587,607,621,657,677,689,695,711,731,743,765
%N A050200 Sum of three consecutive primes.
%C A050200 The occurrence of multiples of 3 in the sequence appears to converge to 
about .44
%o A050200 (PARI) sumprime3(n) = { c1=0; c2=0; forprime(x=2,n, s = 
nextprime(x)+nextprime(x+1)+nextprime(x+3); c1++; if(s%3==0,c2++); print1(s" "); 
); print(); print(c2/c1+.0) }
%t A050200 nextprim[n_] := Block[{k = n}, While[! PrimeQ[k], k++]; k]; f[n_] := (x 
= Prime[n]; nextprim[x] + nextprim[x + 1] + nextprim[x + 3]); Table[ f[n], {n, 
54}] (from RGWv Feb 12 2005)
%Y A050200 Cf. A050207.
%K A050200 easy,nonn
%O A050200 1,1
%A A050200 Cino Hilliard (hillcino368(AT)hotmail.com), May 08 2003



זקיר סעידוב - ד"ר/Zakir Seidov Ph.D. wrote:

> Dear SeqFans,
> why these two?
> 
> A050200
> 10,15,23,29,41,47,59,65,81,97,105,119,131,137,153,171,187,
> 195,209,223,231,245,261,283,299,311,317,329,335,367,389,405,
> 425,437,457,465,483,497,513,531,551,563,581,587,607,621,657,
> 677,689,695,711,731,743,765
> Sum of three consecutive primes.
> 
> A034961
> 10,15,23,31,41,49,59,71,83,97,109,121,131,143,159,173,187,
> 199,211,223,235,251,269,287,301,311,319,329,349,371,395,407,
> 425,439,457,471,487,503,519,533,551,565,581,589,607,633,661,
> 679,689,701,713,731,749,771
> Sums of three consecutive primes
> 
> I think that A034961 is OK and should be kept in OEIS.
> 
> zak
> 
> 
>  
> 
>  
>