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A272478 Primes with a prime number of binary digits, and with a prime number of 1's and a prime number of 0's. 1
17, 19, 79, 103, 107, 109, 5119, 6079, 6911, 7039, 7103, 7151, 7159, 7919, 7927, 7933, 8059, 8111, 8123, 8167, 8171, 8179, 442367, 458239, 458719, 458747, 487423, 491503, 499711, 507839, 507901, 515839, 516091, 520063, 523007, 523261, 523519, 523759, 523771, 523903, 524219, 524221, 524269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If the sum of primes p and q is a prime r, then one of p and q must be 2. - N. J. A. Sloane, May 01 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10859

Michel Marcus, 3 primes

EXAMPLE

a(3) = 79, its binary representation is 1001111 with (prime) 7 digits, (prime) 5 1's and (prime) 2 0's.

MATHEMATICA

Select[Table[Prime[j], {j, 1, 120000}], PrimeQ[Total@IntegerDigits[#, 2]]&&PrimeQ[Length@IntegerDigits[#, 2]]&&PrimeQ[(Length@IntegerDigits[#, 2]-Total@IntegerDigits[#, 2])]&]

Select[Prime@ Range[10^5], And[PrimeQ@ Total@ #, PrimeQ@ First@ #, PrimeQ@ Last@ #] &@ DigitCount[#, 2] &] (* Michael De Vlieger, May 01 2016 *)

PROG

(PARI) isok(n) = isprime(n) && isprime(#binary(n)) && isprime(hammingweight(n)) && isprime(#binary(n) - hammingweight(n)); \\ Michel Marcus, May 01 2016

CROSSREFS

Cf. A052294, A095079, A272441.

Sequence in context: A226681 A005808 A180559 * A028489 A210242 A165320

Adjacent sequences:  A272475 A272476 A272477 * A272479 A272480 A272481

KEYWORD

nonn,base

AUTHOR

Andres Cicuttin, May 01 2016

STATUS

approved

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Last modified October 20 02:07 EDT 2019. Contains 328244 sequences. (Running on oeis4.)