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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309374 Numbers k such that k+j is prime for every j, where 1 <= j < k and gcd(j,k) = 1. 0
2, 4, 6, 10, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It was conjectured by Recamán Santos in 1976 and proved by Hausman and Shapiro in 1978 that 12 is the largest k possible.
Pomerance & Penney (1977) reported in a letter that they have proved that the conjecture is true. - Amiram Eldar, May 15 2020
REFERENCES
Paulo Ribenboim, The New Book of Prime Number Records, Third ed., Springer-Verlag New York, 1996, p. 42.
LINKS
Miriam Hausman and Harold N. Shapiro, Adding totitives, Mathematics Magazine, Vol. 51, No. 5 (1978), pp. 284-288.
Carl Pomerance and David E. Penney, Santos' conjecture, News & Letters, Mathematics Magazine, Vol. 50, No. 2 (1977), p. 107.
Bernardo Recamán Santos, Twelve and its totatives, Mathematics Magazine, Vol. 49, No. 5 (1976), pp. 239-240.
EXAMPLE
For k = 12 the numbers j are {1,5,7,11} and the numbers k+j are {13,17,19,23}, which are all prime.
MATHEMATICA
sQ[n_/; n>1]:=AllTrue[n+Select[Range[n-1], GCD[#, n]==1&], PrimeQ]; Select[Range[12], sQ]
CROSSREFS
Sequence in context: A067852 A253968 A102025 * A226295 A090127 A057910
KEYWORD
nonn,fini,full
AUTHOR
Ivan N. Ianakiev, Jul 26 2019
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 December 4 05:46 EST 2023. Contains 367541 sequences. (Running on oeis4.)