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.

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

Robert Price, Table of n, a(n) for n = 1..2000

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

Cf. A175791, A180517 thru A180559, A175789, A180561.

Sequence in context: A300372 A132973 A107760 * A320085 A358691 A172368

Adjacent sequences: A180557 A180558 A180559 * A180561 A180562 A180563

Keyword

base,nonn

Author

Zak Seidov and Robert G. Wilson v, Sep 09 2010

Extensions

a(101)-a(104) corrected by Robert Price, Oct 31 2023

Status

approved