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%I #25 Dec 03 2023 17:04:19
%S 4,9,118,514,1202,9662,46418,198878,273386,717818,717818,270893786,
%T 1009201118,1009201118,68668578806,421210555538,421210555538,
%U 81550619289662,645040014922382,645040014922382,645040014922382
%N a(n) is the least semiprime that is the first of n consecutive semiprimes s(1) ... s(n) such that s(i) - prime(i) are all equal.
%e a(3) = 118 because 118, 119, 121 are consecutive semiprimes with 118 - 2 = 119 - 3 = 121 - 5 = 116, and this is the first semiprime that works.
%p P:= select(isprime, [2,seq(i,i=3..10^6,2)]):
%p SP:= select(t -> numtheory:-bigomega(t)=2, [$4..10^7]):
%p nSP:= nops(SP);
%p t:= 1: k0:= 1: R:= 4: tmax:= 1: d:= 2:
%p for k from 2 to nSP do
%p if SP[k]-P[k-k0+1] = d then
%p t:= t+1;
%p if t > tmax then R:= R, SP[k0]; tmax:= t; fi;
%p else
%p t:= 1; k0:= k; d:= SP[k] - 2;
%p fi
%p od:
%p R;
%Y All terms are in A001358 and (except for the initial term 4) A070552.
%K nonn,more
%O 1,1
%A _Robert Israel_, Nov 05 2023
%E a(12) from _David A. Corneth_, Nov 05 2023
%E a(13)-a(15) from _Daniel Suteu_, Nov 18 2023
%E a(16)-a(18) from _Martin Ehrenstein_, Dec 01 2023
%E a(19)-a(21) from _Martin Ehrenstein_, Dec 03 2023
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