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 A303705 a(1) = 3; a(n) is the smallest prime such that gcd(a(i)-1, a(n)-1) = 2 holds for 1 <= i < n. 1
 3, 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 239, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1223, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2243, 2447 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) exists for all n, which is easily shown by Dirichlet's theorem on arithmetic progressions. Apart from 3, the first term that is not a term in A005385 is 239. The first term in A092307 and A119660 (apart from 2) that is not a term here is 443. Clearly all safe primes are in this sequence, and all terms except a(2) = 5 are == 3 (mod 4). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(13) = 239 since that lcm(a(1)-1, a(2)-1, ..., a(12)-1) = 2^2*3*5*11*23*29*41*53*83*89*113 and 239-1 = 2*7*17. MAPLE A[1]:= 3: L:= 2: for i from 2 to 100 do   p:= nextprime(A[i-1]);   while igcd(L, p-1) > 2 do p:= nextprime(p) od:   A[i]:= p;   L:= ilcm(L, p-1); od: seq(A[i], i=1..100); # Robert Israel, Apr 29 2018 CROSSREFS Cf. A005385, A079148, A092307, A119660. Sequence in context: A038890 A227240 A226017 * A265687 A023368 A295973 Adjacent sequences:  A303702 A303703 A303704 * A303706 A303707 A303708 KEYWORD nonn AUTHOR Jianing Song, Apr 29 2018 EXTENSIONS Corrected by Robert Israel, Apr 29 2018 STATUS approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)