A283928 Numbers k such that prime(k) divides primorial(j) + 1 for exactly three integers j.

436, 2753, 13396, 19960, 24293, 26157, 58492, 58723, 61935, 121992, 136592, 145803, 149027, 159752, 179811, 180776, 184575, 194499, 262321, 268645, 280911, 315198, 327876, 339951, 364307, 390394, 413010, 433626, 444744, 492661, 510412, 518156, 541925, 542177

Offset: 1

Author

Jon E. Schoenfield, Mar 24 2017

Keywords

• nonn

Comments

As used here, "primorial(j)" refers to the product of the first j primes, i.e., A002110(j).

Primorial(j) + 1 is the j-th Euclid number, A006862(j).

Examples

			436 is in this sequence because prime(436) = 3041 divides primorial(j) + 1 for exactly three integers j: 206, 263, and 409.
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
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..150

Crossrefs

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).

Cf. A000040, A002110, A006862, A113165.

Programs

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

Extensions

a(10)-a(34) from Jon E. Schoenfield, Apr 02 2017