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%I #72 Mar 20 2022 14:27:57
%S 436,2753,13396,19960,24293,26157,58492,58723,61935,121992,136592,
%T 145803,149027,159752,179811,180776,184575,194499,262321,268645,
%U 280911,315198,327876,339951,364307,390394,413010,433626,444744,492661,510412,518156,541925,542177
%N Numbers k such that prime(k) divides primorial(j) + 1 for exactly three integers j.
%C As used here, "primorial(j)" refers to the product of the first j primes, i.e., A002110(j).
%C Primorial(j) + 1 is the j-th Euclid number, A006862(j).
%H Giovanni Resta, <a href="/A283928/b283928.txt">Table of n, a(n) for n = 1..150</a>
%e 436 is in this sequence because prime(436) = 3041 divides primorial(j) + 1 for exactly three integers j: 206, 263, and 409.
%e 180707 is not in this sequence because prime(180707) = 2464853 divides primorial(j) + 1 for exactly five integers j: 75366, 79914, 139731, 139990, and 175013. - _Jon E. Schoenfield_, Mar 30 2017
%o (Magma) countReqd:=3; kMaxTest:=20000; P:=PrimesInInterval(2,NthPrime(kMaxTest)); itos:=IntegerToString; a:=[]; for k in [1..kMaxTest] do p:=P[k]; pMinus1:=p-1; primorialModp:=1; jSuccess:=[]; if primorialModp eq pMinus1 then jSuccess:=[1]; end if; for j in [1..k-1] do primorialModp:=(primorialModp*P[j]) mod p; if primorialModp eq pMinus1 then jSuccess[#jSuccess+1]:=j; end if; end for; if #jSuccess eq countReqd then a[#a+1]:=k; "a("*itos(#a)*") = " * itos(k) * "; successes at j =", jSuccess; end if; end for; a; // _Jon E. Schoenfield_, Mar 25 2017
%Y Subsequence of A279097 (which includes all numbers k such that prime(k) divides primorial(j) + 1 for one or more integers j); cf. A279098 (exactly one integer j), A279099 (exactly two).
%Y Cf. A000040, A002110, A006862, A113165.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Mar 24 2017
%E a(10)-a(34) from _Jon E. Schoenfield_, Apr 02 2017
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