A290639 a(n) = largest number <= prime(n) such that 1 + a(1)*a(2)*...*a(n) is prime.
2, 3, 5, 7, 11, 11, 16, 15, 21, 22, 30, 36, 41, 43, 34, 36, 56, 60, 48, 55, 54, 59, 57, 75, 42, 93, 93, 103, 104, 75, 126, 123, 133, 129, 148, 104, 146, 162, 159, 128, 177, 159, 153, 175, 184, 187, 193, 223, 210, 151, 164, 170, 240, 239, 254, 261, 201, 261, 253, 254, 170, 255, 297, 257, 270, 291, 309, 267, 341, 310, 261, 316, 363, 329, 373, 361, 327, 381, 373, 401, 346, 351, 379
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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Maple
A[1]:= 2: P:= 2: for n from 2 to 200 do for k from ithprime(n) by -1 do if isprime(1+P*k) then A[n]:= k; P:= P*k; break fi od; od: seq(A[i],i=1..200); # Robert Israel, Aug 08 2017 -
Mathematica
a[1] = 2; a[n_] := a[n] = Module[{k = Prime[n], r = Product[a[i], {i, 1, n - 1}]}, While[! PrimeQ[1 + k*r], k--]; k]; Array[a, 100] (* Amiram Eldar, Jan 19 2023 *) nxt[{n_,p_,a_}]:=Module[{k=Prime[n+1]},While[!PrimeQ[1+p*k],k--];{n+1,p*k,k}]; NestList[nxt,{1,2,2},85][[;;,3]] (* Harvey P. Dale, Jul 27 2025 *)
Extensions
More terms from Robert Israel, Aug 08 2017
Comments