login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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) from Jon E. Schoenfield, Mar 26 2017

a(11) from Jon E. Schoenfield, Mar 27 2017

a(12)-a(14) from Jon E. Schoenfield, Mar 29 2017

a(15)-a(20) from Jon E. Schoenfield, Mar 30 2017

a(21)-a(25) from Jon E. Schoenfield, Mar 31 2017

a(26)-a(29) from Jon E. Schoenfield, Apr 01 2017

a(30)-a(34) from Jon E. Schoenfield, Apr 02 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 07:21 EDT 2018. Contains 316337 sequences. (Running on oeis4.)