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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 *)