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1, 4, 18, 33, 42, 44, 50, 55, 90, 98, 195, 288, 311, 395, 457, 521, 859, 891, 898, 1848, 1876, 2717, 3688, 3757, 3796, 4733, 5243, 5301, 5321, 6295, 6389, 6434, 6526, 6556, 6634, 6650, 6690, 7318, 7938, 8027, 9013, 9293, 9327, 9409, 9462, 9883, 10053
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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First differences are Pi's shadow. Never twice the same integer in sequence or first differences.
a(20) is 1848, not 993, since the latter would leave out the next 0 in Pi. - Michael S. Branicky, Jun 15 2021
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The first line hereunder is the sequence, the second line are the first differences:
1.4..18..33.42.44.50.55..90.98..195..288..311...
.3.14..15..9..2..6..5..35..8..97...93...23 <-- Pi shadow
(Pi=3.141592653589793238462643383279502884197169399...)
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = Block[{c = RealDigits[Pi, 10, 300][[1]], k = 1, t = Table[a[i], {i, n - 1}]}, d = Drop[t, 1] - Drop[t, -1]; b = Drop[c, Length[ Flatten[ IntegerDigits /@ d]]]; e = Union[ Join[t, d]]; While[f = FromDigits[ Take[b, k]]; Position[e, f] != {} || b[[k + 1]] == 0, k++ ]; f + a[n - 1]]; Table[ a[n], {n, 47}] (* Robert G. Wilson v *)
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PROG
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# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
# with open('pi-billion.txt', 'r') as f: pi = f.readline()
from sympy import S
pi = str(S.Pi.n(3*10**5)).replace('.', '') # alternatively
def aupton(terms):
global pi
alst, idx, seen = [1], 0, {0, 1}
while len(alst) < terms:
k = 1
while int(pi[idx:idx+k]) in seen or pi[idx+k] == '0': k += 1
diffn = int(digits_of_pi[idx:idx+k])
alst.append(alst[-1] + diffn)
seen |= {diffn, alst[-1]}
idx += k
return alst
print(aupton(47)) # Michael S. Branicky, Jun 15 2021
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CROSSREFS
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Cf. A000796.
Sequence in context: A095823 A092116 A083969 * A124978 A031081 A009956
Adjacent sequences: A110618 A110619 A110620 * A110622 A110623 A110624
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KEYWORD
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easy,nonn,base
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AUTHOR
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Eric Angelini and Alexandre Wajnberg, Sep 14 2005
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EXTENSIONS
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More terms from Robert G. Wilson v, Oct 10 2005
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STATUS
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approved
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