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Search: id:A106525
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| A106525 |
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Values of a in a^2-49=2b^2. |
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+0
2
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| 9, 11, 21, 43, 57, 119, 249, 331, 693, 1451, 1929, 4039, 8457, 11243, 23541, 49291, 65529, 137207, 287289, 381931, 799701, 1674443, 2226057, 4660999, 9759369, 12974411, 27166293, 56881771, 75620409, 158336759, 331531257, 440748043
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OFFSET
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1,1
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COMMENT
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The sums of the consecutive integers in the following sequences will be squares: n,i >=1 if mod(i,3)=0 : 7n+1,7n+2, ..., a(i)n + (A001541(i/3)-1)/2 if mod(i,3)=1 or 2 : 7n+4, 7n+5, ..., a(i)n + (a(i)-1)/2
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FORMULA
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a(3n)=A001541(n)*7 for n>=2: a(3n+1)=(A001541(n+2)+A001541(n-1)+A001541(n)-A001541(n+1))/2 a(3n+2)=(A001541(n+2)+A001541(n-1)-A001541(n)+A001541(n+1))/2
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EXAMPLE
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In the following, aa(n) denotes A001541(n)
a(9)=693; as mod(9,3)=0, a(9)=aa(3)*7=99*7=693, also 693^2-49=2*490^2
a(10)=1451; as mod(10,3)=1, a(10)=(aa(5)+aa(2)+aa(3)-aa(4))/2 =(3363+17+99-577)/2=1451, also 1451^2-49=2*1026^2
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CROSSREFS
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Cf. A001541, A106525.
Sequence in context: A046259 A074345 A022323 this_sequence A103510 A130730 A153697
Adjacent sequences: A106522 A106523 A106524 this_sequence A106526 A106527 A106528
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KEYWORD
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nonn
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AUTHOR
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Andras Erszegi (erszegi.andras(AT)chello.hu), May 07 2005
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