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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 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

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