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A090709 Primes whose decimal representation is a valid number in base 6 and interpreted as such is again a prime. 9
2, 3, 5, 11, 31, 101, 151, 211, 241, 251, 331, 421, 431, 521, 1021, 1151, 1231, 1321, 2011, 2131, 2311, 2351, 2441, 2531, 2551, 3041, 3221, 3251, 3301, 3541, 4021, 4111, 4201, 4421, 4441, 4451, 5011, 5021, 5101, 5231, 5441, 5531, 10331, 11131, 11311 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
31 is prime in decimal and a valid number in base 6: 31_6 = 19, a prime.
MATHEMATICA
Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 6], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *)
vn6pQ[n_]:=Module[{idn=IntegerDigits[n]}, Max[idn]<6&&PrimeQ[ FromDigits[ idn, 6]]]; Select[Prime[Range[1500]], vn6pQ] (* Harvey P. Dale, Jul 10 2015 *)
PROG
(Python)
from gmpy2 import digits, is_prime
A090709_list = [n for n in (int(digits(d, 6)) for d in range(10**6) if is_prime(d)) if is_prime(n)] # Chai Wah Wu, Apr 09 2016
(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, 6), if(isprime(t=fromdigits(digits(p, 6), 10)), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016
(Magma) [[n:n in PrimesUpTo(12000)| Max(Intseq(n, 10)) le 5 and IsPrime(Seqint(Intseq(Seqint(Intseq(n), 6))))]; // Marius A. Burtea, Jun 30 2019
CROSSREFS
Sequence in context: A072535 A073680 A079557 * A357220 A112279 A130166
KEYWORD
base,nonn
AUTHOR
Cino Hilliard, Jan 18 2004
EXTENSIONS
Following suggestions by V.J. Pohjola and Donovan Johnson, name, example and offset corrected by M. F. Hasler, Jan 03 2014
STATUS
approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)