1,2

First differences are sqrt(2)'s shadow. Never twice the same integer in sequence or first differences.

G. C. Greubel, Table of n, a(n) for n = 1..5000

The first line below is the sequence, the second gives the first differences:

1..15...157..170.175.181.183.186.193..223.232..282.286.294

.14..142...13...5...6...2...3...7...30...9...50...4...8 <- sqrt(2) shadow

sqrt(2) = 1.4142135623730950488016887242096980785696718753769...

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 *)

Cf. A002193.

Sequence in context: A341918 A099915 A385813 * A016304 A016849 A300077

Adjacent sequences: A110554 A110555 A110556 * A110558 A110559 A110560

easy,nonn,base

Eric Angelini and Alexandre Wajnberg, Sep 14 2005

More terms from Robert G. Wilson v, Oct 10 2005

approved