A090253 -id:A090253 - cp's OEIS frontend

A152445 a(0) = a(1) = 1. For n >= 2, a(n) = the smallest prime >= a(n-1)*a(n-2).

1, 1, 2, 2, 5, 11, 59, 653, 38543, 25168589, 970072925867, 24415366771173991757, 23684686279828682858246730078719, 578270302382209771209755703072864217352250067119367

Offset: 0

Leroy Quet, Dec 04 2008

nonn

Cf. A090253, A152446.

A152445 := proc(n) option remember ; if n <= 1 then 1; else nextprime(procname(n-1)*procname(n-2)-1) ; fi; end: for n from 0 to 15 do printf("%d,",A152445(n)) ; od; # R. J. Mathar, Dec 05 2008

a = {1, 1, 2, 2}; Do[AppendTo[a, Prime[PrimePi[a[[ -1]]*a[[ -2]]] + 1]], {7}]; a (* Stefan Steinerberger, Dec 06 2008 *)
nxt[{a_,b_}]:={b,NextPrime[a*b-1]}; NestList[nxt,{1,1},15][[All,1]] (* Harvey P. Dale, Jun 30 2020 *)

Extended beyond a(7) by R. J. Mathar, Stefan Steinerberger and Ray Chandler, Dec 05 2008

A382261 a(n) = floor(x^(phi^n)), where phi = (1+sqrt(5))/2 and x is the constant A382260.

Original entry on oeis.org

2, 3, 7, 23, 163, 3803, 620549, 2359981439, 1464484123012601, 3456155348019933976288373, 5061484633840283809323162088349619180781, 17493277186167814180104995425523045477935447066389138909089293633

Offset: 1

Thomas Scheuerle, Mar 19 2025

nonn

Conjecture: All terms are prime numbers. For details see A382260.

Cf. A001622, A059784, A051254, A243358, A382260. A090253.

Cf. A090253 ( similar growth ).

nextprime(a(n-2)*a(n-1)) <= a(n) < nextprime((a(n-2)+1)*a(n-1)).

cp's OEIS Frontend

A152445 a(0) = a(1) = 1. For n >= 2, a(n) = the smallest prime >= a(n-1)*a(n-2).

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A382261 a(n) = floor(x^(phi^n)), where phi = (1+sqrt(5))/2 and x is the constant A382260.

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