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A110557 Shadow of sqrt(2). +0
1
1, 15, 157, 170, 175, 181, 183, 186, 193, 223, 232, 282, 286, 294, 374, 390, 478, 550, 970, 1066, 2046, 2124, 2180, 3147, 3165, 3240, 3277, 3346, 3826, 3899, 3916, 3982, 4061, 4798, 5788, 6520, 6567, 6651, 6713, 6723, 6793, 6831, 7681, 8068, 8121, 8164 (list; graph; listen)
OFFSET

1,2

COMMENT

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

EXAMPLE

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...

MATHEMATICA

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 *)

CROSSREFS

Cf. A002193.

Sequence in context: A098685 A006096 A099915 this_sequence A016304 A016849 A016297

Adjacent sequences: A110554 A110555 A110556 this_sequence A110558 A110559 A110560

KEYWORD

easy,nonn,base

AUTHOR

Eric Angelini & Alexandre Wajnberg (eric.angelini(AT)kntv.be), Sep 14 2005

EXTENSIONS

More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 10 2005

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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