A072537 a(1) = 2, a(2) = 3 and a(n) = the smallest prime which is a linear combination of all previous terms with all coefficients >= 1.

2, 3, 5, 13, 23, 53, 101, 211, 419, 839, 1669, 3343, 6689, 13381, 26759, 53527, 107053, 214129, 428221, 856459, 1712899, 3425803, 6851617, 13703231, 27406471, 54812957, 109625881, 219251761, 438503537, 877007063, 1754014121

Offset: 1

Author

Amarnath Murthy, Aug 03 2002

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..3318

Crossrefs

Cf. A072536, A000040, A062391, A151800.

Programs

Maple

A[1]:= 2: A[2]:= 3: S:= 5:
for i from 3 to 50 do
  if S::even then A[i]:= nextprime(S+1)
else A[i]:= nextprime(S-1)
  fi;
S:= S + A[i]
od:
seq(A[i],i=1..50); # Robert Israel, May 01 2019

Formula

For n >= 3, a(n) = A151800(S+(-1)^S) where S = Sum_{i=1..n-1} a(i). - Robert Israel, May 01 2019

Extensions

Corrected and extended by Sascha Kurz, Feb 12 2003