A090710 Primes with digits less than 7 whose decimal representation is also a prime when interpreted in base 7.

2, 3, 5, 23, 41, 43, 61, 113, 131, 241, 313, 401, 421, 443, 461, 463, 661, 1013, 1033, 1051, 1123, 1231, 1301, 1433, 1453, 1543, 1613, 2111, 2131, 2153, 2203, 2333, 2441, 2531, 2551, 3121, 3163, 3251, 3323, 3433, 3541, 4001, 4111, 4153, 4201, 4241, 4421

Offset

1,1

Comments

Note that the definition of, e.g., A090714 works "the other way round". - M. F. Hasler, Jan 03 2014

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

23 is a prime and a valid number in base 7, and 23 [base 7] = 17 [base 10] is again a prime.

Mathematica

Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 7], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *)
FromDigits/@Select[Tuples[{0, 1, 2, 3, 4, 5, 6}, 4], AllTrue[ {FromDigits[ #], FromDigits[ #, 7]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 29 2015 *)

Prog

(PARI) is_A090710(p, b=7)=vecmax(d=digits(p))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p) \\ M. F. Hasler, Jan 03 2014
(PARI) fixBase(n, oldBase, newBase)=my(d=digits(n, oldBase), t=newBase-1); for(i=1, #d, if(d[i]>t, for(j=i, #d, d[j]=t); break)); fromdigits(d, newBase)
list(lim)=my(v=List(), t); forprime(p=2, fixBase(lim\1, 10, 7), if(isprime(t=fromdigits(digits(p, 7), 10)), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016

Crossrefs

Cf. A031974, A089971, A089981, A090707, A090708, A090709, A235394, A235395, A000040.

Sequence in context: A215313 A215317 A104736 * A153477 A386139 A080016

Adjacent sequences: A090707 A090708 A090709 * A090711 A090712 A090713

Keyword

base,nonn

Author

Cino Hilliard, Jan 18 2004

Extensions

Name, example and offset corrected by M. F. Hasler, Jan 03 2014

Status

approved