A376406
a(0) = 1, and for n > 0, a(n) = A019565(Sum_{i=0..n-1} a(i)), where A019565 is the base-2 exp-function.
Original entry on oeis.org
1, 2, 6, 14, 330, 10166, 12075690, 1174153011328084322, 73582975079922326904310062621361286633125176265747127754
Offset: 0
Starting with a(0) = 1, we take partial sums of previous terms, and apply A019565 to get the next term, and in the rightmost column, we "unbox" that term by applying A048675 to get A376407(n), which thus gives the partial sums of a(0)..a(n-1):
a(0) = 1 -> 0
a(1) = A019565(1) = 2, -> 1 = 1
a(2) = A019565(1+2) = 6, -> 3 = 1+2
a(3) = A019565(1+2+6) = 14, -> 9 = 1+2+6
a(4) = A019565(1+2+6+14) = 330, -> 23 = 1+2+6+14
a(5) = A019565(1+2+6+14+330) = 10166, -> 353 = 1+2+6+14+330
a(6) = A019565(1+2+6+14+330+10166) = 12075690, -> 10519 = 1+2+6+14+330+10166
etc.
Cf.
A376407 (=
A048675(a(n)), also gives the partial sums from its second term onward).
-
up_to = 12;
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A376406list(up_to) = { my(v=vector(up_to), s=1); v[1]=1; for(n=2,up_to,v[n] = A019565(s); s += v[n]); (v); };
v376406 = A376406list(1+up_to);
A376406(n) = v376406[1+n];
A376403
a(0) = 0, and for n > 0, a(n) = a(n-1) + A276076(a(n-1)), where A276076 is the factorial base exp-function.
Original entry on oeis.org
0, 1, 3, 9, 39, 1089, 520179, 1466909163669354042297
Offset: 0
Cf. also
A143293 (when prepended with 0, an analogous sequence for
A276086).
A376400
a(0) = 1, and for n > 0, a(n) = a(n-1) * A276076(a(n-1)), where A276076 is the factorial base exp-function.
Original entry on oeis.org
1, 2, 6, 30, 1050, 70814493750, 7568077812763134673885891483463343434987134201379042046671543939118568739667281250
Offset: 0
Cf.
A376401 (=
A276075(a(n)), also gives the partial sums from its second term onward).
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A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
A376400(n) = if(!n,1,my(x=A376400(n-1)); x*A276076(x));
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