

A169655


Numbers n such that 2^n is in A054861.


5



0, 1, 2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 41, 42, 43, 45, 46, 47, 49, 53, 54, 55, 56, 58, 59, 60, 62, 64, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 82, 84, 85, 87, 88, 89, 91, 93
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OFFSET

1,3


COMMENTS

For a prime p, we call a number pcompact if the exponent of p in the factorization of the number is a power of two. However, if m=k!, then not all exponents of p of the form 2^t are possible. The sequence lists numbers t in possible exponents of the form 2^t of 3 in 3compact factorials k!The question of description of the pcompact factorials is interesting since there exists only finite set of factorials compact over both 2 and an arbitrary fixed odd prime (cf. A177436). On the other hand, there exist infinitely many 2compact factorials. However, up to now it is unknown, whether exist infinitely many pcompact factorials for a fixed odd prime p. It is expected that the answer to be in affirmative.


REFERENCES

V. Shevelev, Compact integers and factorials, Acta Arith., 126.3 (2007), 195236.


LINKS

Table of n, a(n) for n=1..66.


MATHEMATICA

A054861 := (Plus @@ Floor[#/3^Range[Length[IntegerDigits[#, 3]]  1]] &); DeleteCases[Table[n  n Sign[2^n  A054861[2^(n + 1) + NestWhile[# + 1 &, 1, 2^n  A054861[2^(n + 1) + #] >= 0 &]  1]], {n, 1, 125}], 0] (* Peter J. C. Moses, Apr 10 2012 *)


CROSSREFS

Cf. A050376, A054861.
Sequence in context: A264763 A126167 A026260 * A286489 A002153 A047607
Adjacent sequences: A169652 A169653 A169654 * A169656 A169657 A169658


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Apr 05 2010


EXTENSIONS

More terms given by Peter J. C. Moses, Apr 07 2012


STATUS

approved



