A348927 - OEIS

%I #43 Nov 20 2021 11:35:31

%S 2,5,17,347,2903,15373,128981,95285633,2426256797,41193770837,

%T 706748065831,68439250465123,68439250465123

%N a(n) is the smallest prime followed by n prime gaps in arithmetic progression with a common difference of 2.

%C a(n) is the smallest prime p for which the n+1 consecutive primes starting at p can be written as p + c*k + k^2, 0 <= k <= n, for some c >= 0. - _Pontus von Brömssen_, Nov 07 2021

%C 73389327921983 is the smallest prime followed by exactly 12 such gaps. - _Martin Ehrenstein_, Nov 20 2021

%e a(2)=5, the 2 prime gaps after 5 are 2,4.

%e a(3)=17, the 3 prime gaps after 17 are 2,4,6.

%e a(4)=347, the 4 prime gaps after 347 are 2,4,6,8.

%e a(5)=2903, the 5 prime gaps after 2903 are 6,8,10,12,14.

%t Join[{p=2},Table[While[Union@Differences[NextPrime[p,Range[0,n]],2]!={2},p=NextPrime@p];p,{n,2,7}]] (* _Giorgos Kalogeropoulos_, Nov 05 2021 *)

%Y Cf. A349121 (same, but starting prime gap = 2), A001223 (prime gaps), A036263 (2nd differences), A158939 (monotonic increasing), A006560 (consecutive primes in arithmetic progression).

%Y First column of A094749 (except first few terms).

%K nonn,more

%O 1,1

%A _Marc Morgenegg_, Nov 04 2021

%E a(8) from _Giorgos Kalogeropoulos_, Nov 05 2021

%E a(9) from _Pontus von Brömssen_, Nov 07 2021

%E a(10)-a(13) from _Martin Ehrenstein_, Nov 20 2021