A098026 Smallest prime p such that p+1 is the product of exactly n distinct prime numbers.

2, 5, 29, 389, 2309, 30029, 570569, 11741729, 300690389, 10407767369, 239378649509, 9426343036109, 304250263527209, 18740171637257069, 693386350578511589, 37508276737897976009, 2925030695773453637369, 141143645364710083725629, 8327475076517894939812169

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..100

Example

a(4) = 389 because 389+1 = 2*3*5*13.

Mathematica

Generate[pIndex_, i_] := Module[{p2, t}, p2=pIndex; While[p2[[i]]++; Do[p2[[j]]=p2[[i]]+j-i, {j, i+1, Length[p2]}]; t=Times@@Prime[p2]; t<fact*base, AppendTo[s, t]; If[i<Length[p2], Generate[p2, i+1]]]]; fact=2; Table[pin=Range[n]; base=Times@@Prime[pin]; s={base}; Do[Generate[pin, j], {j, n}]; s=Sort[s]; noPrime=True; i=0; While[noPrime&&i<Length[s], i++; noPrime=!PrimeQ[ -1+s[[i]]]]; If[noPrime, -1, -1+s[[i]]], {n, 20}] (* T. D. Noe, Dec 13 2004 *)

Crossrefs

Cf. A073918 (least prime p such that p-1 has exactly n distinct prime factors).

Sequence in context: A191621 A103592 A209428 * A179823 A064098 A181078

Adjacent sequences: A098023 A098024 A098025 * A098027 A098028 A098029

Keyword

nonn

Author

Lekraj Beedassy, Sep 10 2004

Extensions

Corrected and extended by Ray Chandler, Sep 18 2004

Further corrected and extended by T. D. Noe, Dec 13 2004

a(14) corrected and terms a(18) onward added by Max Alekseyev, Mar 16 2023

Status

approved