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
Examples
23 is a prime and a valid number in base 7, and 23 [base 7] = 17 [base 10] is again a prime.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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 *)
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PARI
is_A090710(p,b=7)=vecmax(d=digits(p))
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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
Extensions
Name, example and offset corrected by M. F. Hasler, Jan 03 2014
Comments