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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224070 Sets of four primes such that the sum of any three is prime, ordered first by sum, then lexicographically. 1
5, 7, 17, 19, 7, 11, 13, 23, 7, 13, 17, 23, 5, 13, 19, 29, 5, 11, 13, 43, 11, 13, 19, 29, 5, 7, 19, 47, 5, 17, 19, 37, 7, 11, 19, 41, 11, 17, 19, 31, 5, 11, 31, 37, 5, 13, 23, 43, 11, 13, 17, 43, 11, 13, 23, 37, 13, 17, 23, 31, 7, 11, 19, 53, 7, 11, 29, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..4000

Chris Caldwell and G. L. Honaker, Jr., Prime Curios!

EXAMPLE

The first four terms of the sequence are 5, 7, 17, 19. The sum of any three is prime: 5 + 7 + 17 = 29, 5 + 7 + 19 = 31, 5 + 17 + 19 = 41, 7 + 17 + 19 = 43. This set of four primes has the smallest possible sum, 48, and is unique.

There are two such sets of four primes with sum 72: {5, 11, 13, 43} and {11, 13, 19, 29}. The first set is listed first since it is lexicographically earliest.

MATHEMATICA

MaxSum = 100; nn = PrimePi[MaxSum - 15]; ps = {}; Do[p = Prime[{a, b, c, d}]; If[Total[p] <= MaxSum, AppendTo[ps, p]], {a, 2, nn - 3}, {b, a + 1, nn - 2}, {c, b + 1, nn - 1}, {d, c + 1, nn}]; s = Select[ps, And @@ PrimeQ /@ (Total[#] - #) &]; s2 = SortBy[s, Total]; Flatten[s2] (* T. D. Noe, Apr 01 2013 *)

CROSSREFS

Cf. A000040.

Sequence in context: A064944 A070372 A082818 * A075089 A075305 A140564

Adjacent sequences:  A224067 A224068 A224069 * A224071 A224072 A224073

KEYWORD

nonn

AUTHOR

G. L. Honaker, Jr., Mar 30 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 October 17 14:31 EDT 2019. Contains 328114 sequences. (Running on oeis4.)