A223546
Composite numbers in the sequence A217723.
Original entry on oeis.org
247, 233335657, 6703028887, 7628001653827, 311878265181037, 628284422185342477, 33217442899375387207, 1955977793053588026277, 119244359152460559009547, 7977565910232727614888637, 565918396036931688582304027, 3258940366335958863738288181627
Offset: 1
a(1) = 247 = 13*19 which is the first composite number in sequence A217723.
A285528
Numbers n such that A217723(n) (sum of first n primorial numbers minus 1) is prime.
Original entry on oeis.org
2, 3, 5, 6, 7, 8, 11, 14, 21, 41, 42, 43, 74, 78
Offset: 1
A217723(5) = 2 + 2*3 + 2*3*5 + 2*3*5*7 + 2*3*5*7*11 - 1 = 2557 is prime, thus 5 is in this sequence.
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select(m -> isprime(add(mul(ithprime(i),i=1..j),j=1..m)-1), [$1..89]); # Robert Israel, Apr 20 2017
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primorial[n_] := Product[Prime[i], {i, n}]; a[n_] := Sum[primorial[i], {i, 1, n}]-1; Select[Range[0, 100], PrimeQ[a[#]] &]
(* Second program: *)
Flatten@ Position[Accumulate@ FoldList[#1 #2 &, Prime@ Range@ 200] - 1 /. k_ /; k == 1 || CompositeQ@ k -> 0, m_ /; m != 0] (* Michael De Vlieger, Apr 23 2017 *)
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