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Search: id:A161595
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| A161595 |
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The list of the A values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2. |
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4
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| 1, 16, 271, 4591, 77776, 1317601, 22321441, 378146896, 6406175791, 108526841551, 1838550130576, 31146825378241, 527657481299521, 8939030356713616, 151435858582831951, 2565470565551429551, 43461563755791470416, 736281113282903567521, 12473317362053569177441
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The 2 equations are equivalent to the Pell equation x^2- 285*y^2=1,
with x=(285*k+17)/2 and y=A*B/2, case C=15 in A160682.
Also: the first differences of A078366.
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FORMULA
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A(t+2)=17*A(t+1)-A(t).
a(t)=((285+15*w)*((17+w)/2)^(t-1)+(285-15*w)*((17-w)/2)^(t-1))/570 where w=sqrt(285).
a(t) = ceiling of ((285+15*w)*((17+w)/2)^(t-1))/570;
G.f.: x*(1-x)/(1-17*x+x^2).
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MAPLE
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t:=0: for a from 1 to 1000000 do b:=sqrt((19*a^2-4)/15):
if (trunc(b)=b) then t:=t+1: n:=(a^2-1)/15: print(t, a, b, n): end if: end do:
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CROSSREFS
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Cf. A160682, A161599 (sequence of B), A161583 (sequence of k).
Sequence in context: A113359 A166908 A119290 this_sequence A144660 A158574 A000487
Adjacent sequences: A161592 A161593 A161594 this_sequence A161596 A161597 A161598
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KEYWORD
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nonn
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AUTHOR
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Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 14 2009
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EXTENSIONS
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Edited, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2009
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