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A138152
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A double recursive procedure that produces primes by their gaps in a triangular sequence:a(n, m) = a(n - 1, m) + 10 and a(n,m)+2*Ceiling(log(1+k)),k<=n.
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1
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3, 7, 11, 13, 17, 19, 23, 29, 31, 31, 37, 41, 41, 43, 47, 53, 59, 61, 61, 67, 71, 71, 73, 79, 83, 83, 89, 97, 101, 103, 101, 103, 107, 109, 113, 113, 127, 131, 131, 137, 139, 149, 151, 151, 157, 163, 163, 167, 173, 173, 179, 181, 181, 191, 193, 197, 199
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
{10, 60, 83, 109, 131, 173, 199, 306, 172, 301, 533, 113, 258, 407, 300, 471, 503, 533, 181, 780};
The procedure is based on the Modulo 10 prime ending set {1,3,7,9}
and leaves out {2,5} at the start. To n=20 the precedure produces all of the primes except {2,5}. It also classifies primes by the length of the longest
vector they appear in.
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FORMULA
| a(0,m)={0,1,3,7,9}; a(n, m) = a(n - 1, m) + 10 a(n,m)=If( prime,{a(n,m),a(n,m)+2*Ceiling(log(1+k)),k<=n)
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EXAMPLE
| {3, 7},
{11, 13, 17, 19},
{23, 29, 31},
{31, 37, 41},
{41, 43, 47},
{53, 59, 61},
{61, 67, 71},
{71, 73, 79, 83},
{83, 89},
{97, 101, 103},
{101, 103, 107, 109, 113},
{113},
{127, 131},
{131, 137, 139},
{149, 151},
{151, 157, 163},
{163, 167, 173},
{173, 179, 181},
{181},
{191, 193, 197, 199}
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MATHEMATICA
| a[0, 0] = 0; a[0, 1] = 1; a[0, 2] = 3; a[0, 3] = 7; a[0, 4] = 9; a[n_, m_] := a[n, m] = a[n - 1, m] + 10; a0 = Table[Union[Flatten[Table[If[PrimeQ[a[n, m]] && PrimeQ[a[n, m] + 2*k], {a[n, m], a[n, m] + 2*k}, {}], {m, 0, 4}, {k, 0, Ceiling[Log[1 +n]]}]]], {n, 0, 20}]; Flatten[a0]
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CROSSREFS
| Sequence in context: A111068 A102213 A158942 * A004139 A180346 A020632
Adjacent sequences: A138149 A138150 A138151 * A138153 A138154 A138155
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KEYWORD
| nonn,uned,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 04 2008
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