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 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 Table of n, a(n) for n=1..5. 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 Adjacent sequences: A309371 A309372 A309373 * A309375 A309376 A309377 KEYWORD nonn,fini,full AUTHOR Ivan N. Ianakiev, Jul 26 2019 STATUS approved

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Last modified December 4 05:46 EST 2023. Contains 367541 sequences. (Running on oeis4.)