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A359940
Lexicographically earliest sequence of distinct primes whose partial products lie between noncomposite numbers.
3
2, 3, 5, 19, 11, 7, 31, 23, 193, 67, 367, 131, 317, 1097, 241, 1777, 773, 2819, 2689, 1381, 1741, 3389, 631, 8581, 41, 1553, 2297, 1427, 17053, 1493, 883, 619, 9803, 13331, 26203, 37, 7681, 41269, 1913, 27091, 3079, 31583, 5867, 22409, 13367, 37337, 29573, 6469
OFFSET
1,1
LINKS
EXAMPLE
2 - 1 = 1 and 2 + 1 = 3 are both noncomposite numbers.
2*3 - 1 = 5 and 2*3 + 1 = 7 are both noncomposite numbers.
2*3*5 - 1 = 29 and 2*3*5 + 1 = 31 are both noncomposite numbers.
MAPLE
P:= {seq(ithprime(i), i=2..10^5)}:
R:= 2: s:= 2:
for i from 2 to 100 do
found:= false;
for p in P do
if isprime(p*s-1) and isprime(p*s+1) then R:= R, p; s:= p*s; P:= P minus {p}; found:= true; break fi;
od;
if not found then break fi
od:
R; # Robert Israel, Jan 19 2023
MATHEMATICA
a[1] = 2; a[n_] := a[n] = Module[{t = Table[a[k], {k, 1, n - 1}], p = 2, r}, r = Times @@ t; While[MemberQ[t, p] || ! PrimeQ[r*p - 1] || ! PrimeQ[r*p + 1], p = NextPrime[p]]; p]; Array[a, 50]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 19 2023
STATUS
approved