|
Search: id:A105720
|
|
|
| A105720 |
|
Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes. |
|
+0
5
|
|
| 5, 15, 36, 67, 112, 169, 240, 323, 424, 539, 662, 803, 964, 1133, 1312, 1523, 1746, 1987, 2246, 2519, 2808, 3119, 3436, 3787, 4154, 4529, 4920, 5337, 5770, 6219, 6682, 7173, 7672, 8203, 8760, 9323, 9912, 10517, 11140, 11783, 12450, 13135, 13836
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Cf. A045943 Triangular matchstick numbers: sum of n and next n integers; a(n) are full squares at only(?) three values of n = 3, 6, 4072: {6,13,15735}^2;a(n) are primes at many values of for n = 1,4,16,18,22,36,40,44,52,...: 5,67,1523,1987,3119,9323,11783,14551,21019,...
|
|
FORMULA
|
a(n)=p(n)+p(n+1)+...+p(2n-1)+p(2n), p(k)=k-th prime
a(1)=5; n>1: a(n)=a(n-1)-prime(n-1)+prime(2*n-1)+prime(2*n). [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
|
|
MATHEMATICA
|
a[n_]:=Plus@@Prime[Range[n, 2n]]
a=5; s={5}; Do[a=a-Prime[n]+Prime[2n+1]+Prime[2n+2]; AppendTo[s, a], {n, 10^5}]; [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
|
|
CROSSREFS
|
Cf. A045943.
Cf. A166619, A166620. [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
Sequence in context: A056413 A032276 A065780 this_sequence A011933 A093802 A006008
Adjacent sequences: A105717 A105718 A105719 this_sequence A105721 A105722 A105723
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Zak Seidov (zakseidov(AT)yahoo.com), May 04 2005
|
|
|
Search completed in 0.002 seconds
|
