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A180560
The number of times the n-th 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
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
Index to Primes, Primes that become a different prime under some mapping.
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))))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Oct 31 2023
CROSSREFS
KEYWORD
base,nonn
AUTHOR
EXTENSIONS
a(101)-a(104) corrected by Robert Price, Oct 31 2023
STATUS
approved