A166109 - OEIS

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.

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

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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;

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