

A296474


Decimal expansion of limiting powerratio for A295948; see Comments.


3



7, 4, 3, 2, 1, 3, 8, 6, 5, 6, 0, 2, 2, 4, 6, 4, 6, 9, 8, 6, 0, 3, 7, 4, 4, 7, 6, 2, 9, 9, 9, 1, 5, 0, 0, 0, 7, 5, 5, 1, 2, 5, 5, 0, 7, 1, 9, 6, 0, 8, 2, 8, 5, 9, 9, 8, 0, 3, 1, 0, 5, 5, 1, 5, 0, 6, 3, 4, 8, 4, 1, 8, 0, 3, 4, 0, 8, 6, 9, 6, 6, 3, 4, 8, 6, 3
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OFFSET

1,1


COMMENTS

Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n1) > g. The limiting powerratio for A is the limit as n>oo of a(n)/g^n, assuming that this limit exists. For A = A296948 we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.


LINKS

Table of n, a(n) for n=1..86.


EXAMPLE

limiting powerratio = 7.432138656022464698603744762999150007551...


MATHEMATICA

a[0] = 3; a[1] = 4; b[0] = 1; b[1 ] = 2; b[2] = 5;
a[n_] := a[n] = a[n  1] + a[n  2] + b[n];
j = 1; While[j < 12, k = a[j]  j  1;
While[k < a[j + 1]  j + 1, b[k] = j + k + 2; k++]; j++];
Table[a[n], {n, 0, 15}] (* A295948 *)
z = 2000; g = GoldenRatio; h = Table[N[a[n]/g^n, z], {n, 0, z}];
StringJoin[StringTake[ToString[h[[z]]], 41], "..."]
Take[RealDigits[Last[h], 10][[1]], 120] (* A296474 *)


CROSSREFS

Cf. A001622, A295948, A296473.
Sequence in context: A200121 A198348 A019857 * A194705 A344906 A243309
Adjacent sequences: A296471 A296472 A296473 * A296475 A296476 A296477


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 19 2017


STATUS

approved



