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A036261
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Triangle of numbers arising from Gilbreath's conjecture: successive absolute differences of primes (read by antidiagonals upwards, omitting the initial row of primes).
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13
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1, 1, 2, 1, 0, 2, 1, 2, 2, 4, 1, 2, 0, 2, 2, 1, 2, 0, 0, 2, 4, 1, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 2, 4, 1, 2, 0, 0, 0, 0, 0, 2, 6, 1, 0, 2, 2, 2, 2, 2, 2, 4, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 4, 6, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 4, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 4
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, A10.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 410.
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LINKS
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T. D. Noe, Rows n=1..100 of triangle, flattened
A. M. Odlyzko, Iterated absolute values of differences of consecutive primes, Math. Comp. 61 (1993), 373-380.
Wikipedia, Gilbreath's conjecture.
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EXAMPLE
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Table begins (conjecture is leading term is always 1):
2 3 5 7 11 13 17 19 23 ...
1 2 2 4 2 4 2 4 ...
1 0 2 2 2 2 2 ...
1 2 0 0 0, 0 ...
1 2 0 0 0 ...
1 2 0 0 ...
...
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MATHEMATICA
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max = 15; triangle = Rest[ NestList[ Abs[ Differences[#] ]& , Prime[ Range[max] ], max] ]; Flatten[ Table[ triangle[[n-k+1, k]], {n, 1, max-1}, {k, 1, n}]] (* Jean-François Alcover, Jan 23 2012 *)
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CROSSREFS
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See A036262, which is the main entry for this array.
Sequence in context: A035443 A180430 A246369 * A140575 A091917 A025657
Adjacent sequences: A036258 A036259 A036260 * A036262 A036263 A036264
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KEYWORD
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tabl,easy,nice,nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Naohiro Nomoto, May 22 2001
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STATUS
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approved
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