A266331 a(n) is the integer part of r^n where r^2 = Sum_{n>=1} 1/a(n).

1, 2, 3, 5, 8, 13, 20, 31, 49, 75, 116, 179, 277, 427, 658, 1014, 1564, 2410, 3716, 5727, 8828, 13607, 20974, 32328, 49829, 76805, 118383, 182469, 281247, 433499, 668171, 1029882, 1587403, 2446735, 3771261, 5812811, 8959543, 13809740, 21285562, 32808377, 50569000, 77944233, 120138887, 185175372, 285418976, 439928870, 678081791, 1045157403, 1610947251, 2483024123, 3827194710, 5899024182, 9092426420

Offset

1,2

Links

Table of n, a(n) for n=1..53.

Example

The decimal expansion of the constant r where
  r^2 = Sum_{n>=1} 1/[r^n]
begins:
r = 1.54134415118405676117240176536725460162533305165007\
62370966466687126323131372907582654421737525227402\
10192334607267409158392268142586609884312549625161\
21506724007030622882124813044489353916060663230110\
27308560544967802158740044767804169229121426750823\
57644257675943363311242990660223884728481289718990\
99327899421359649328564149987903390825529247758514\
60735850775493331380497311992503361576346218279976\
05645547570287129278274604187536184112176387833291\
85603999054392419841604159463398200203997944803454\
18425909199967800608414423950419889683123004053225\
51628328325921625213161265843364187664239692679133\
78513294659135630061049758456921571790081814747933\
56662679514697664220527288408290298696275446845537\
82221222016040792497786370547407535128976231014195\
28424538734155908632125120724333307147756074998970\
77269230880274065525902832192928532158680079354731\
84681991892727311569600167711260764708905745119208\
50225118393692057423981577550768255645970307508134\
83605351471230633327963097939033535495224207747888...
and
r^2 = 2.37574179238930042560404761867505903636416446875240\
59957559631203234553844077058553274372039964629798\
98357510834612648469470712686851783754235510227750\
90565187608960242393885456328850305615661618592478\
73235190508707789175624418288724279603877433574612\
00324833857381306242732279124873337660083461284883\
95010233009726083527596303538620762218988473225493\
16815052124106064266646624452168065606080470528823\
03804763445360193037282349286239255543016012568922\
76447370868505160365197032313357253107326606199028\
91449896203777054304426301504840031610887915406529\
11878473573221422011200005578382585467361212596995\
47193768339648938955481145460447849072516182832187\
92809353106444677117815846842683730516029679123528\
58098510651879670934972910687177653654664326362582\
16226232499815417804811450182494166404793120242518\
75307338374850069542730971375347317365956348323759\
17794972304079787244456530277492351694360051870511\
98939251737291171103913987697505739506874361694475\
47117869988610908667102907924401481944676104994477...

Crossrefs

Cf. A066173.

Sequence in context: A361721 A173597 A059923 * A055805 A023437 A322332

Adjacent sequences: A266328 A266329 A266330 * A266332 A266333 A266334

Keyword

nonn

Author

Paul D. Hanna, Jan 14 2016

Status

approved