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Consider the number of lines in the Pratt certificate for the n-th prime (A037202). This sequence shows where 2n first occurs.
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%I #5 Jul 03 2014 16:18:28

%S 1,2,4,9,14,34,61,120,215,690,1144,2584,5626,13709,31275,63461,145767,

%T 340332,649190,1703684,4218462,10675070,22892978

%N Consider the number of lines in the Pratt certificate for the n-th prime (A037202). This sequence shows where 2n first occurs.

%C See comment section of A037202.

%C a(n) ~ 2*a(n-1).

%F Also PrimePi( A037231 ).

%t a[1] = 1; a[n_] := a[n] = 1 + Plus @@ (a@ PrimePi@# & /@ First /@ FactorInteger[ Prime@ n - 1]); k = 1; t = Table[0, {1000}]; While[k < 1000000000000001, If[a@ k < 1001 && t[[a[k]/2]] == 0, t[[a[k]/2]] = k; Print[{a@k, k}]]; k++]; t

%Y Cf. A037202, A037231.

%K nonn,more

%O 0,2

%A _Joerg Arndt_ and _Robert G. Wilson v_, Jul 02 2014