

A180560


The number of times the nth prime, p, can become a different prime under any mapping of some single decimal digit <=> with some other single decimal digit.


46



3, 3, 3, 3, 0, 9, 8, 6, 7, 5, 5, 7, 5, 8, 7, 7, 5, 4, 6, 6, 9, 7, 7, 5, 6, 4, 7, 12, 10, 6, 6, 5, 10, 9, 6, 6, 9, 9, 12, 7, 10, 6, 6, 7, 9, 3, 6, 7, 7, 3, 4, 6, 8, 6, 4, 7, 4, 6, 6, 5, 7, 5, 8, 4, 5, 7, 5, 7, 10, 6, 5, 7, 8, 3, 8, 5, 6, 8, 8, 8, 8, 7, 7, 3, 9, 6, 2, 6, 9, 7, 9, 6, 3, 7, 3, 6, 7, 6, 6, 7, 7, 5, 9, 5
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OFFSET

1,1


COMMENTS

First occurrence of k, from 0 to 45: 5, 195, 87, 1, 18, 10, 8, 9, 7, 6, 29, 172, 28, 1275, 7666, 1279, ..., .


LINKS



EXAMPLE

2 can become either 3, 5 or 7 under the proper mapping, therefore a(1)=3.
11 cannot become any other prime regardless of the mapping, therefore a(5)=0.


MATHEMATICA

fQ[n_] := Block[{id = IntegerDigits@n}, (MemberQ[id, s[[1]]]  MemberQ[id, s[[2]]]) && PrimeQ[ FromDigits[id /. {s[[1]] > s[[2]], s[[2]] > s[[1]] }] ]]; t = Sort@ Flatten@ Table[s = {j, k}; Select[ Prime@ Range@ 100, fQ], {j, 0, 8}, {k, j + 1, 9}]; Table[ Length@ Position[t, Prime@ n], {n, 100}]


PROG

(Python)
from sympy import isprime, prime
def a(n):
s = str(prime(n))
return len(set(t for t in (s.translate({ord(c):ord(d), ord(d):ord(c)}) for c in set(s) for d in "0123456789" if d!=c) if isprime(int(t))))


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



