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Search: id:A036262
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| A036262 |
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Triangle of numbers arising from Gilbreath's conjecture: successive absolute differences of primes. |
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15
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| 2, 1, 3, 1, 2, 5, 1, 0, 2, 7, 1, 2, 2, 4, 11, 1, 2, 0, 2, 2, 13, 1, 2, 0, 0, 2, 4, 17, 1, 2, 0, 0, 0, 2, 2, 19, 1, 2, 0, 0, 0, 0, 2, 4, 23, 1, 2, 0, 0, 0, 0, 0, 2, 6, 29, 1, 0, 2, 2, 2, 2, 2, 2, 4, 2, 31, 1, 0, 0, 2, 0, 2, 0, 2, 0, 4, 6, 37, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 4, 41, 1, 0, 0, 0, 0, 2, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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The conjecture is that the leading term is always 1.
Odlyzko has checked it for primes up to pi(10^13) = 3*10^11.
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REFERENCES
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R. K. Guy, Unsolved Problems Number Theory, A10.
R. B. Killgrove and K. E. Ralston, On a conjecture concerning the primes, Math.Tables Aids Comput. 13(1959), 121-122.
H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 208.
F. Proth, Sur la serie des nombres premiers, Nouv. Corresp. Math., 4 (1878) 236-240.
W. Sierpinski, L'induction incomplete dans la theorie des nombres, Scripta Math. 28 (1967), 5-13.
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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.
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Eric Weisstein's World of Mathematics, 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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CROSSREFS
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Cf. A036261, A036277, A054977.
Sequence in context: A133737 A125047 A045898 this_sequence A046924 A108415 A136644
Adjacent sequences: A036259 A036260 A036261 this_sequence A036263 A036264 A036265
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KEYWORD
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tabl,easy,nice,nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
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