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

1,1

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).

Links

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

Example

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

Prog

(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

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.

Sequence in context: A260012 A234221 A255777 * A278176 A243233 A216988

Adjacent sequences: A283925 A283926 A283927 * A283929 A283930 A283931

Keyword

nonn

Author

Jon E. Schoenfield, Mar 24 2017

Extensions

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

Status

approved