The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136191 Primes p such that 2p-3 and 2p+3 are both prime (A092110), with last decimal being 3. 4
 13, 43, 53, 113, 193, 223, 283, 563, 613, 643, 743, 773, 1033, 1193, 1453, 1483, 1543, 1583, 1663, 1733, 2143, 2393, 2503, 2843, 3163, 3413, 3433, 3793, 3823, 4133, 4463, 4483, 4523, 4603, 4673, 4813, 5443, 5743, 5953, 6073, 6133, 6163, 6553, 6733, 6863 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Except for p=5, the decimals in A092110 end in 3 or 7. Theorem: If in the triple (2n-3,n,2n+3) all numbers are primes then n=5 or the decimal representation of n ends in 3 or 7. Proof: Consider Q=(2n-3)n(2n+3), by hypothesis factorized into primes. If n is prime, n=10k+r with r=1,3,7 or 9. We want to exclude r=1 and r=9. Case n=10k+1. Then Q=5(-1+6k+240k^2+800k^3) and 5 is a factor; thus 2n-3=5 or n=5 or 2n+1=5 : this means n=4 (not prime); or n=5 (included); or n=2 (impossible, because 2n-3=1). Case n=10k+9. Then Q=5(567+1926k+2160k^2+800k^3) and 5 is a factor; the arguments, for the previous case, also hold. LINKS Table of n, a(n) for n=1..45. PROG (PARI) isok(n) = (n % 10 == 3) && isprime(n) && isprime(2*n-3) && isprime(2*n+3); \\ Michel Marcus, Sep 02 2013 CROSSREFS Cf. A092110, A136192. Sequence in context: A340480 A129811 A108545 * A268483 A039318 A146507 Adjacent sequences: A136188 A136189 A136190 * A136192 A136193 A136194 KEYWORD base,nonn AUTHOR Carlos Alves, Dec 20 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.

Last modified May 19 10:22 EDT 2024. Contains 372683 sequences. (Running on oeis4.)