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 A166109 a(1)=5. For n >= 2, a(n) = the smallest prime p > a(n-1) where neither p+1 nor p-1 is divisible by any (earlier) term of this sequence. 1
 5, 7, 17, 23, 37, 53, 157, 163, 173, 193, 227, 233, 257, 263, 283, 353, 383, 397, 457, 487, 523, 557, 563, 607, 677, 683, 733, 787, 823, 857, 863, 877, 947, 983, 997, 1033, 1097, 1117, 1153, 1187, 1193, 1237, 1277, 1283, 1297, 1307, 1423, 1433, 1447, 1453 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence would have terminated after only one term if a(1) equaled 2 or 3. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(5) = 37. So we want to look at the primes > 37 to get a(6). 41 - 1 is divisible by a(1)=5. (And 41+1 is divisible by a(2)=7.) 43-1 is divisible by a(2)=7. 47-1 is divisible by a(4)=23. By 53-1 is not divisible by any earlier terms of the sequence, and 53+1 is not divisible by any earlier terms of the sequence. So a(6) = 53. MAPLE Res:= 5: S:= 5: p:= 5: count:= 1: while count < 100 do p:= nextprime(p); if igcd((p+1)*(p-1), S) = 1 then count:= count+1; Res:= Res, p; S:= S*p; fi od: Res; # Robert Israel, Jun 16 2019 CROSSREFS Sequence in context: A191145 A145354 A214345 * A157755 A265812 A128352 Adjacent sequences: A166106 A166107 A166108 * A166110 A166111 A166112 KEYWORD nonn AUTHOR Leroy Quet, Oct 06 2009 EXTENSIONS Extended by Ray Chandler, Mar 12 2010 STATUS approved

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Last modified February 21 19:37 EST 2024. Contains 370237 sequences. (Running on oeis4.)