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 A283928 Numbers k such that prime(k) divides primorial(j) + 1 for exactly three integers j. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 1 18:25 EDT 2023. Contains 365828 sequences. (Running on oeis4.)