login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A136204 Primes p such that 3p-2 and 3p+2 are primes (see A125272) and its decimal representation ends in 7. 1
7, 37, 127, 167, 257, 337, 757, 797, 887, 1307, 1597, 1657, 1667, 2347, 2557, 2897, 2927, 3067, 4297, 4327, 4877, 5087, 5147, 5227, 5417, 5857, 6337, 6827, 6917, 6967, 7127, 7187, 7547, 7687, 7867, 7877, 8147, 8447, 8527, 8647, 9857, 10037, 10687 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Theorem: If in the triple (3n-2,n,3n+2) all numbers are primes, then n=5 or the decimal representation of n ends in 3 or 7. Proof: Similar to A136191. Alternative Mathematica proof: Table[nn = 10k + r; Intersection (AT)(AT) (Divisors[CoefficientList[(3nn - 2) nn(3nn + 2), k]]), {r, 1, 9, 2}]; This gives {{1, 5}, {1}, {1, 5}, {1}, {1, 5}}. Therefore only r=3 and r=7 allow nontrivial divisors (excluding nn=5 itself).

LINKS

Table of n, a(n) for n=1..43.

MATHEMATICA

TPrimeQ = (PrimeQ[ # - 2] && PrimeQ[ #/3] && PrimeQ[ # + 2]) &; Select[Select[Range[100000], TPrimeQ]/3, Mod[ #, 10] == 7 &]

CROSSREFS

Cf. A136191, A136192, A125272.

Sequence in context: A106064 A282001 A038862 * A139891 A082113 A196597

Adjacent sequences:  A136201 A136202 A136203 * A136205 A136206 A136207

KEYWORD

nonn,base

AUTHOR

Carlos Alves, Dec 21 2007

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 17:07 EDT 2022. Contains 353847 sequences. (Running on oeis4.)