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A036955
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Numbers whose base-4 representation is the decimal representation of a prime.
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1
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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
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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FromDigits[IntegerDigits[#], 4]&/@Select[Prime[Range[2000]], Max[ IntegerDigits[ #]]<4&] (* Harvey P. Dale, May 02 2015 *)
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PROG
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(PARI) is(n)=isprime(sum(i=1, #n=digits(n, 4), n[i]*10^(#n-i))) \\ M. F. Hasler, Jul 25 2015
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Offset corrected to 1 and minor edits by M. F. Hasler, Jul 25 2015
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STATUS
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approved
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