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%I #15 Jun 15 2021 11:04:49
%S 1,15,157,170,175,181,183,186,193,223,232,282,286,294,374,390,478,550,
%T 970,1066,2046,2124,2180,3147,3165,3240,3277,3346,3826,3899,3916,3982,
%U 4061,4798,5788,6520,6567,6651,6713,6723,6793,6831,7681,8068,8121,8164
%N Shadow of sqrt(2).
%C First differences are sqrt(2)'s shadow. Never twice the same integer in sequence or first differences.
%H G. C. Greubel, <a href="/A110557/b110557.txt">Table of n, a(n) for n = 1..5000</a>
%e The first line below is the sequence, the second gives the first differences:
%e 1..15...157..170.175.181.183.186.193..223.232..282.286.294
%e .14..142...13...5...6...2...3...7...30...9...50...4...8 <- sqrt(2) shadow
%e sqrt(2) = 1.4142135623730950488016887242096980785696718753769...
%t a[1] = 1; a[n_] := a[n] = Block[{c = RealDigits[ Sqrt[2], 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, 46}] (* _Robert G. Wilson v_, Oct 10 2005 *)
%Y Cf. A002193.
%K easy,nonn,base
%O 1,2
%A _Eric Angelini_ and _Alexandre Wajnberg_, Sep 14 2005
%E More terms from _Robert G. Wilson v_, Oct 10 2005
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