A065727 - OEIS

A065727

Primes p such that the decimal expansion of its base-9 conversion is also prime.

2, 3, 5, 7, 37, 43, 61, 109, 127, 199, 271, 277, 379, 457, 487, 523, 541, 613, 619, 673, 727, 757, 883, 907, 919, 991, 997, 1033, 1117, 1249, 1447, 1483, 1531, 1549, 1567, 1627, 1693, 1699, 1747, 1753, 1987, 2053, 2161, 2221, 2287, 2341, 2347, 2437, 2473

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

In general rebase notation (Marc LeBrun): p9 = (9) [p] (10).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

E.g., 997_10 = 1327_9 is prime, and so is 1327_10.

MATHEMATICA

Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ]

NestList[NestWhile[NextPrime, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 9]]] &, 2] &, 2, 48] (* Jan Mangaldan, Jul 01 2020 *)

Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 9], 10]]&] (* Harvey P. Dale, Sep 19 2021 *)

PROG

(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 9); if (isprime(b), write("b065727.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 28 2009

(PARI) isok(p) = isprime(p) && isprime(fromdigits(digits(p, 9))); \\ Michel Marcus, Jul 02 2020

CROSSREFS

Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065361.

Intersection of A000040 and A036964.

Sequence in context: A274678 A048415 A029974 * A090713 A090912 A048416

Adjacent sequences: A065724 A065725 A065726 * A065728 A065729 A065730

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Nov 15 2001

STATUS

approved