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A frugal sequence (Posted on 2012-09-14) Difficulty: 3 of 5
Find the longest(?) string of consecutive frugal numbers.

Def: A frugal number is a natural number that has more digits than the number of digits in its prime factorization (including exponents). For example, 128=2^7 and 29282=2*11^4

  Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)
Solution: (Hide)
Pinch shows that, under a plausible hypothesis related to the twin prime conjecture, there are arbitrarily long sequences of consecutive economical numbers, and exhibits such a sequence of length nine starting at 1034429177995381247.
Therefore - there is no "longest", but longest known so far.

SEE ALSO: oeis -economical numbers

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/Tipsre(4): SolutionAdy TZIDON2017-03-18 10:45:24
re(4): interesting side topic -- economical numbers -- transcription error compoundedCharlie2012-09-15 15:29:05
re(3): interesting side topic -- economical numbers -- transcription error compoundedbroll2012-09-15 11:00:30
Some Thoughtsre(2): interesting side topic -- economical numbers -- transcription error compoundedCharlie2012-09-15 10:33:20
Some Thoughtsre: interesting side topic -- economical numbersDej Mar2012-09-15 06:40:03
Some Thoughtsinteresting side topic -- economical numbersCharlie2012-09-15 01:35:11
Some Thoughtsre: computer results so farCharlie2012-09-14 18:01:25
Some Thoughtscomputer results so farCharlie2012-09-14 15:59:58
re(3): SolutionCharlie2012-09-14 15:57:10
re(2): SolutionAdy TZIDON2012-09-14 14:19:47
Hints/Tipspossible approachbroll2012-09-14 12:09:13
re: Solutionbroll2012-09-14 11:52:53
SolutionChris, PhD2012-09-14 10:21:40
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