Template:Sequence of the Day for April 30

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Intended for: April 30, 2013

Timetable

First draft entered by Alonso del Arte on April 6, 2012 ✓
Draft reviewed by Daniel Forgues on April 26, 2012 ✓
Draft to be approved by March 30, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A038458: Decimal expansion of Smarandache's constant.

0.567148130202...

Given two consecutive primes $\scriptstyle p \,$ and $\scriptstyle q \,$ , what is the smallest positive real number $\scriptstyle x \,$ such that $\scriptstyle q^x - p^x \,=\, 1 \,$ ? If $\scriptstyle p \,=\, 113 \,$ and $\scriptstyle q \,=\, 127 \,$ , then the answer is Smarandache's constant. (We verify that $\scriptstyle 113^x \,\approx\, 14.60157$ and $\scriptstyle 127^x \,\approx\, 15.60157$ .) Sukanto Bhattacharya conjectures that this number is irrational.