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A281299 Primes p whose binary representation p_2 is the decimal representation of a prime q; and also the sum of the decimal digits of p equals the sum of the digits of p_2. 0
5011, 7001, 11251, 22501, 32303, 32411, 90031, 101107, 104123, 108011, 111323, 121343, 122131, 124001, 125101, 141023, 224011, 233021, 235003, 241141, 321203, 324011, 421303, 432031, 442201, 510331, 511213, 520411, 801011, 1000183, 1000541, 1001191, 1005223, 1006231 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A037308 and A065720.

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

a(1) = 5011 is a prime;

5011_2 = 1001110010011_10 is a prime;

5 + 0 + 1 + 1 = 7;

1 + 0 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 0 + 0 + 1 + 1 = 7; both the digit sums are equal.

MATHEMATICA

Select[Prime[Range[1000000]], PrimeQ[FromDigits[IntegerDigits[#, 2]]] && Plus @@ IntegerDigits[#] == Plus @@ IntegerDigits[FromDigits[IntegerDigits[#, 2]]] &]

PROG

(PARI) eva(n) = subst(Pol(n), x, 10)

is(n) = ispseudoprime(n) && ispseudoprime(eva(binary(n))) && sumdigits(n)==sumdigits(eva(binary(n))) \\ Felix Fröhlich, Jan 19 2017

CROSSREFS

Cf. A000040, A033548, A037308, A065720, A089971.

Sequence in context: A217985 A201178 A252216 * A112139 A188241 A252162

Adjacent sequences:  A281296 A281297 A281298 * A281300 A281301 A281302

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Jan 19 2017

STATUS

approved

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Last modified October 26 11:29 EDT 2020. Contains 338027 sequences. (Running on oeis4.)