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A292163 a(n) is the least prime p such that the orderly concatenation of the n successive powers of p yields a prime number; a(n)=0 if n is a multiple of 6. 0
3, 3, 337, 23, 0, 373, 37, 839, 421, 7, 0, 1447, 2113, 29, 43, 17, 0, 1789, 523, 84737, 7669, 397, 0, 3851, 3583, 99149, 146023, 157, 0, 14173, 38329, 1229, 8017, 1021, 0, 18979, 5437, 17207, 6571, 47, 0, 347, 43669, 25847, 257353, 2887, 0, 33889, 71287 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

See in the Prime Puzzle link the discussion for when n is a multiple of 6.

LINKS

Table of n, a(n) for n=2..50.

Carlos Rivera, Puzzle 892. Primes as a concatenation of a series of powers of a prime, The Prime Puzzles and Problems Connection.

EXAMPLE

For n=2, the concatenation of 3^0 and 3^1 is 13 which is prime (while 12 was not prime); so a(2) = 3.

For n=3, the concatenation of 3^0, 3^1 and 3^2 is 139 which is prime (while 124 was not prime); so a(3) = 3.

MAPLE

g:= proc(p, n) local i, t;

  t:= p^(n-1):

  for i from n-2 to 0 by -1 do

    t:= t + 10^(1+ilog10(t))*p^i

  od;

  t

end proc:

f:= proc(n)

  local p;

  if n mod 6 = 0 then return 0 fi;

  p:= 3;

  while not isprime(g(p, n)) do

    p:= nextprime(p);

    if n mod 3 = 0 then while p mod 3 = 1 do p:= nextprime(p) od fi:

  od;

  p

end proc:

map(f, [$2..30]); # Robert Israel, Sep 10 2017

PROG

(PARI) pconc(p, n) = {my(s = "1"); for (k=1, n, s = concat(s, Str(p^k)); ); eval(s); }

a(n) = {if (!(n % 6), return (0)); n --; my(p = 2); while (! isprime(pconc(p, n)), p = nextprime(p+1)); p; }

CROSSREFS

Cf. A047253.

Sequence in context: A113466 A007301 A009715 * A242886 A221947 A138662

Adjacent sequences:  A292160 A292161 A292162 * A292164 A292165 A292166

KEYWORD

nonn,base

AUTHOR

Michel Marcus, Sep 10 2017

EXTENSIONS

a(27)-a(50) from Robert Israel, Sep 10 2017

STATUS

approved

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Last modified December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)