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A089981 Primes whose decimal representation also represents a prime in base 3. 74
2, 2111, 2221, 10211, 12011, 12211, 20201, 21011, 21101, 21211, 22111, 101021, 101111, 102101, 102121, 110221, 111121, 111211, 120011, 120121, 121001, 121021, 122011, 201101, 202001, 202021, 210011, 210101, 1000211, 1010201, 1012201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A065721 for the primes given by these terms considered as numbers written in base 3, i.e., the sequence with the definition "working in the opposite sense". - M. F. Hasler, Jan 05 2014

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Alejandro J. Becerra Jr., Python code for computing terms of A089971, A089981, A090707-A090710, A235394-A235395.

EXAMPLE

2111 is a prime and its decimal representation is also a valid base-3 representation (because all digits are < 3), and 2111[3] = 67[10] is again a prime. Therefore 2111 is in the sequence.

MATHEMATICA

Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 3], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *)

PROG

(PARI) is_A089981(p)=vecmax(d=digits(p))<3&&isprime(vector(#d, i, 3^(#d-i))*d~)&&isprime(p) \\ "d" is implicitly declared local. Putting isprime(p) to the end improves performance when the function is applied to primes only, as below, or to very large numbers. - M. F. Hasler, Jan 05 2014

(PARI) forprime(p=2, 1e6, is_A089981(p)&&print1(p", ")) \\ - M. F. Hasler, Jan 05 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, 3), if(isprime(t=fromdigits(digits(p, 3), 10)), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016

CROSSREFS

Cf. A031974, A089971, A090707, A090708, A090709, A090710, A235394, A235395, A000040 and further references therein.

Sequence in context: A275002 A004813 A342294 * A028487 A073476 A051103

Adjacent sequences:  A089978 A089979 A089980 * A089982 A089983 A089984

KEYWORD

base,nonn

AUTHOR

Cino Hilliard, Jan 18 2004

EXTENSIONS

Definition and example reworded, offset corrected and cross-references added by M. F. Hasler, Jan 05 2014

STATUS

approved

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)