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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A300372 A132973 A107760 * A320085 A358691 A172368
KEYWORD
base,nonn
AUTHOR
EXTENSIONS
a(101)-a(104) corrected by Robert Price, Oct 31 2023
STATUS
approved

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Last modified April 25 11:06 EDT 2024. Contains 371967 sequences. (Running on oeis4.)