

A155548


Primes p such that p and the pth prime have the same number of prime digits.


3



2, 3, 7, 17, 37, 47, 73, 83, 89, 97, 113, 163, 179, 193, 197, 251, 347, 359, 383, 397, 421, 431, 443, 487, 541, 547, 571, 593, 607, 617, 631, 653, 673, 677, 719, 727, 743, 751, 761, 787, 821, 829, 857, 877, 881, 883, 947, 971, 1009, 1013, 1019, 1021, 1051, 1087
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Prime digit = 2, 3, 5 or 7.


LINKS



EXAMPLE

2 is a term because 2 is prime, prime(2)=3, and 2 and 3 each have 1 prime digit.
3 is a term because 3 is prime, prime(3)=5, and 3 and 5 each have 1 prime digit.
4 is not a term because 4 is not prime.
5 is prime, but prime(5)=11, and 5 has 1 prime digit while 11 has 0 prime digits, so 5 is not a term.


MAPLE

mm := proc (m) options operator, arrow: convert(m, base, 10) end proc: a := proc (n) local t, s, j: t := 0: s := 0: for j to nops(mm(n)) do if isprime(mm(n)[j]) = true then t := t+1 else end if end do: for j to nops(mm(ithprime(n))) do if isprime(mm(ithprime(n))[j]) = true then s := s+1 else end if end do: if isprime(n) = true and t = s then n else end if end proc: seq(a(n), n = 1 .. 1300); # Emeric Deutsch, Jan 28 2009


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS

Corrected (added 761, 857; deleted 977) and extended by Emeric Deutsch, Jan 28 2009


STATUS

approved



