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a(1)=1, a(2)=2 and a(n+1) is minimal such that there are a(n-1) primes strictly between a(n) and a(n+1).
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%I #13 Nov 29 2019 22:06:39

%S 1,2,4,8,20,54,152,464,1532,5334,19764,77042,316760,1361630,6129422,

%T 28709012,139999730,707500404,3705539918,20045427240,111972406422,

%U 644198989898,3815636759538,23221092882642,145131413157282

%N a(1)=1, a(2)=2 and a(n+1) is minimal such that there are a(n-1) primes strictly between a(n) and a(n+1).

%C 2 is the only prime in the sequence.

%e There are 4 primes (11,13,17,19) between 8 and the next term 20.

%t a[1]=1; a[2]=2; a[n_] := a[n]=1+Prime[1+Sum[a[i], {i, 1, n-2}]]

%Y Cf. A082278.

%K more,nonn

%O 1,2

%A _Amarnath Murthy_, Apr 13 2003

%E Better description from _Vladeta Jovovic_, Apr 15 2003

%E a(24)-a(25) from _Chai Wah Wu_, Nov 29 2019