A367075 - OEIS

%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