

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
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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 2391 = 2*7*17.


MAPLE

A[1]:= 3: L:= 2:
for i from 2 to 100 do
p:= nextprime(A[i1]);
while igcd(L, p1) > 2 do p:= nextprime(p) od:
A[i]:= p;
L:= ilcm(L, p1);
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



