login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187762 a(n) = smallest final prime in a chain of 2n+1 consecutive primes such that sum of the last 1, 3, 5, ..., 2n+1 terms in the sequence is also a prime. 0
2, 11, 17, 47, 71, 157, 157, 167, 203569, 203569, 2803083484951 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture: a(n) exists for all n. (This may follow from the Green-Tao theorem, Dirichlet's theorem and Dickson's conjecture.)

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

Consider the chain of following consecutive prime numbers 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157

Take the sum of an odd number of primes out of this sequence starting at the end:

S(1) = 157

S(3) = 157 + 151 + 149 = 457

S(5) = 157 + 151 + 149 + 139 + 137 = 733

S(7) = 157 + 151 + 149 + 139 + 137 + 131 +127 = 991

S(9) = 157 + 151 + 149 + 139 + 137 + 131 +127 + 113 + 109 = 1213

S(11) = 157 + 151 + 149 + 139 + 137 + 131 +127 + 113 + 109 + 107 + 103 = 1423

All of these are prime numbers.

Currently a(10) is the last known term, a chain of 21 primes found after searching up to 4*10^13. The 21 consecutive primes are 2803083484321, 2803083484343, 2803083484349, 2803083484363, 2803083484391, 2803083484429, 2803083484499, 2803083484507, 2803083484633, 2803083484637, 2803083484639, 2803083484673, 2803083484697, 2803083484703, 2803083484763, 2803083484777, 2803083484781, 2803083484819, 2803083484921, 2803083484937, 2803083484951, where the sums S(21), S(19), S(17), S(15) . . . . to S(1): 58864753177133, 53258586208469, 47652419239757, 42046252270937, 36440085301931, 30833918332661, 25227751363349, 19621584393949, 14015417424409, 8409250454809, 2803083484951 respectively are also primes.

MATHEMATICA

(* This program is not convenient for n > 9 *) run[m_, n_] := Prime /@ Range[m + 2n, m, -1]; ok[ru_List] := (test = True; For[k = 1, k <= Length[ru], k = k+2, s = Total[ru[[1 ;; k]]]; If[! PrimeQ[s], test = False; Break[]]]; test); a[n_] := a[n] = Catch[For[m = 1, m <= 10^5, m++, r = run[m, n]; If[ok[r ], Throw[r[[1]]]]]]; Table[Print[a[n]]; a[n], {n, 0, 9}] (* Jean-Fran├žois Alcover, Jan 08 2013 *)

CROSSREFS

Cf. A182121.

Sequence in context: A234647 A106949 A236687 * A217306 A106981 A176985

Adjacent sequences:  A187759 A187760 A187761 * A187763 A187764 A187765

KEYWORD

nonn

AUTHOR

Vikram Pandya, Jan 04 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)