

A036955


Numbers whose base4 representation is the decimal representation of a prime.


1



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 55, 61, 71, 73, 77, 79, 83, 91, 97, 103, 107, 109, 113, 115, 121, 131, 133, 149, 151, 157, 163, 167, 169, 181, 191, 193, 197, 203, 217, 227, 233, 241, 247, 251, 253, 275, 277, 287, 293, 299, 305, 307, 311, 313
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OFFSET

1,1


COMMENTS

All terms are congruent to 1 or 3 (mod 4) (except for the first one) and congruent to 1 or 5 (mod 6) (except for the first two); although not all terms are prime, as e.g., 55, 77, 91, 115, 121, 133, 169, 203, ...  M. F. Hasler, Jul 25 2015
Numbers (not necessarily prime) which are prime if written in base 4 and reinterpreted in base 10. Numbers n such that A007090(n) is in A000040.  R. J. Mathar, Jul 28 2015


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

55 is in the sequence because 55_10 = 313_4 and 313_10 is prime.
313 is in the sequence because 313_10 = 10321_4 and 10321_10 is prime.
31 is not in the sequence because 31_10 = 133_4 and 133_10 = 7*19 is not prime.


MATHEMATICA

FromDigits[IntegerDigits[#], 4]&/@Select[Prime[Range[2000]], Max[ IntegerDigits[ #]]<4&] (* Harvey P. Dale, May 02 2015 *)


PROG

(PARI) is(n)=isprime(sum(i=1, #n=digits(n, 4), n[i]*10^(#ni))) \\ M. F. Hasler, Jul 25 2015


CROSSREFS

Cf. A004678, A036952  A036964, A107715.
Sequence in context: A129621 A316504 A077500 * A040179 A040986 A040990
Adjacent sequences: A036952 A036953 A036954 * A036956 A036957 A036958


KEYWORD

nonn,base


AUTHOR

Patrick De Geest, Jan 04 1999


EXTENSIONS

Offset corrected to 1 and minor edits by M. F. Hasler, Jul 25 2015


STATUS

approved



