Panfigural primes

Stargate38 · 2015-02-16, 21:18

A "panfigural" prime in base-b is, like pandigital primes, a prime that uses all the possible figures of said base at least once. For example:

pan(b)=smallest panfigural prime in base-b

pan(2)=101₂=5₁₀
pan(3)=102₃=11₁₀
pan(4)=10123₄=283₁₀
pan(5)=101234₅=3319₁₀
pan(6)=1013425₆=48761₁₀
pan(7)=10223465₇=863231₁₀
pan(8)=101234567₈=17119607₁₀
pan(9)=1012346785₉=393474749₁₀
pan(10)=10123457689₁₀ (the smallest pandigital prime)

Find the smallest panfigural primes for bases 11-94. Figures for said bases are below:

Code:

0         1         2         3         4         5         6         7         8         9
0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz`~!@#$%^&*()-_=+[]{}\|;:,.<>/?'"

Also, What's the easiest way to do this?

Batalov · 2015-02-16, 23:10

Quote:

Originally Posted by Stargate38

A "panfigural" prime in base-b is, like pandigital primes, a prime that uses all the possible figures of said base at least once. For example:

pan(b)=smallest panfigural prime in base-b

pan(2)=101₂=5₁₀
...

pan(2)=10₂=2₁₀ rather?

Stargate38 · 2015-02-17, 00:00

Oops! I went for b+1 figures, thinking that was the smallest possible size, and overlooked it.

CRGreathouse · 2015-02-17, 05:38

The first 100 are here
https://oeis.org/A185122
due to Per H. Lundow.

2015-02-16, 21:18	#1
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 297₁₆ Posts	Panfigural primes A "panfigural" prime in base-b is, like pandigital primes, a prime that uses all the possible figures of said base at least once. For example: pan(b)=smallest panfigural prime in base-b pan(2)=101₂=5₁₀ pan(3)=102₃=11₁₀ pan(4)=10123₄=283₁₀ pan(5)=101234₅=3319₁₀ pan(6)=1013425₆=48761₁₀ pan(7)=10223465₇=863231₁₀ pan(8)=101234567₈=17119607₁₀ pan(9)=1012346785₉=393474749₁₀ pan(10)=10123457689₁₀ (the smallest pandigital prime) Find the smallest panfigural primes for bases 11-94. Figures for said bases are below: Code: 0 1 2 3 4 5 6 7 8 9 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz`~!@#$%^&()-_=+[]{}\\|;:,.<>/?'" Also, What's the easiest way to do this? Last fiddled with by Stargate38 on 2015-02-16 at 21:19*

2015-02-17, 00:00	#3
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 297₁₆ Posts	Overlooked one Oops! I went for b+1 figures, thinking that was the smallest possible size, and overlooked it. Last fiddled with by Stargate38 on 2015-02-17 at 00:02

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2015-02-17, 05:38	#4
CRGreathouse Aug 2006 5979₁₀ Posts	The first 100 are here https://oeis.org/A185122 due to Per H. Lundow.