

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.


45



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, 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

Table of n, a(n) for n=1..103.
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}]


CROSSREFS

Cf. A175791, A180517 thru A180559, A175789, A180561.
Sequence in context: A300372 A132973 A107760 * A320085 A172368 A138070
Adjacent sequences: A180557 A180558 A180559 * A180561 A180562 A180563


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



