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A053403
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Consider the set P of pairs (a,b) generated by the rules: (1,1) is in P; if (a,b) is in P then (b,a+b) is in P; if (a,b) and (a',b') are in P then (aa', bb') is in P. Sequence gives numbers not appearing in P.
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3
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7, 11, 19, 29, 31, 47, 49, 53, 67, 71, 73, 79, 87, 91, 103, 119, 127, 131, 137, 139, 141, 142, 143, 146, 147, 151, 155, 179, 191, 193, 201, 203, 211, 213, 219, 223, 227, 229, 235, 237, 239, 247, 251, 265, 271, 301, 329, 331, 337, 341, 343, 347, 355, 358, 359
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OFFSET
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1,1
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COMMENTS
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Sequence has 508 known terms, the largest of which is 55487. Conjecturally it is finite. If it is and 55487 is the largest term, then the function the number of groups of order n takes on all positive integers as values.
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REFERENCES
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R. Keith Dennis, The number of groups of order n, Cambridge Tracts in Mathematics, number 173.
Claudia A. Spiro, Local distribution results for the group-counting function at positive integers. In Proceedings of the Sundance conference on combinatorics and related topics (Sundance, Utah, 1985). Congr. Numer. 50 (1985), 107-110. MR0833542 (87g:11117).
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LINKS
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EXAMPLE
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The pairs with b <= 7 are (1,1), (1,2), (1,4), (2,3), (2,6), (3,5), and (4,5). Since none of these has b = 7, 7 can never appear in P. - Charlie Neder, Feb 01 2019
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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R. Keith Dennis (dennis(AT)math.cornell.edu), Jan 07 2000
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STATUS
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approved
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