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A090710 Primes with digits less than 7 whose decimal representation is also a prime when interpreted in base 7. 9
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 (list; graph; refs; listen; history; text; internal format)
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 A080016 A171432

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

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Last modified December 1 07:20 EST 2022. Contains 358454 sequences. (Running on oeis4.)