A270268 For any prime consider the concatenation of its digits written in base b, and convert it to base 10: sequence lists primes that produce other primes for every base b, 3 <= b <= 9, under this process.

1221221, 14201591, 39741391, 220290431, 554011061, 570264221, 623215031, 700648051, 705042731, 1021490321, 1046114051, 1107832991, 1136676421, 1192829461, 1221992311, 1362343261, 1712449621, 1723640701, 1724002061, 1773228511, 2122510631, 3008249821, 3120492691

Offset

1,1

Comments

1221992311 is the first prime that gives a prime for b = 2 too.

Links

Table of n, a(n) for n=1..23.

Example

Digits of 39741391:
in base 3 are 10, 100, 21, 11, 1, 10, 100, 1 and their concatenation is 1010021111101001 which is the prime 16090759 in base 10;
in base 4 are 3, 21, 13, 10, 1, 3, 21, 1 and their concatenation is 321131013211 which is the prime 15061477 in base 10;
in base 5 are 3, 14, 12, 4, 1, 3, 14, 1 and their concatenation is 31412413141 which is the prime 32935421 in base 10;
in base 6 are 3, 13, 11, 4, 1, 3, 13, 1 and their concatenation is 31311413131 which is the prime 196874767 in base 10;
in base 7 are 3, 12, 10, 4, 1, 3, 12, 1 and their concatenation is 31210413121 which is the prime 900203221 in base 10;
in base 8 are 3, 11, 7, 4, 1, 3, 11, 1 and their concatenation is 3117413111 which is the prime 423499337 in base 10;
in base 9 are 3, 10, 7, 4, 1, 3, 10, 1 and their concatenation is 3107413101 which is the prime 1209273301 in base 10.

Maple

P:= proc(q) local a, b, c, h, k, n, ok;  for n from 1 by 2 to q do
if isprime(n) then ok:=1; for h from 3 to 9 do a:=[]; b:=n;
for k from 1 to ilog10(n)+1 do c:=convert(b mod 10, base, h);
if c=[] then c:=[0]; fi; b:=trunc(b/10);
a:=[op(a), op(c)]; od; a:=convert(a, base, h, 10); b:=0;
for k from nops(a) by -1 to 1 do b:=b*10+a[k]; od;
if not isprime(b) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: P(10^12);

Crossrefs

Cf. A000040.

Sequence in context: A235910 A234997 A213703 * A257152 A257159 A254741

Adjacent sequences: A270265 A270266 A270267 * A270269 A270270 A270271

Keyword

nonn,base

Author

Paolo P. Lava, Mar 14 2016

Status

approved