A281621 The smallest of four consecutive odd numbers with binary representations which, read in decimal, are prime.

173599, 418727, 1120979, 1283423, 1660677, 2755429, 3884515, 4704667, 5050711, 5058587, 5197757, 6613127, 6983139, 7423731, 10052677, 10311443, 11315237, 11769187, 15186613, 16145627, 18620507, 19579079, 19624723, 20823831, 20929957, 21387095, 21606883, 23517507

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..676

Example

a(1) = 173599 is the smallest in set of 4 consecutive odd numbers {173599, 173601, 173603, 173605} whose binary representations respectively are {101010011000011111, 101010011000100001, 101010011000100011, 101010011000100101} which are all prime when read in decimal.

Mathematica

Select[Range[-1, 30000001, 2], PrimeQ[FromDigits[IntegerDigits[(#), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 2), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 4), 2]]] && PrimeQ[FromDigits[IntegerDigits[(# + 6), 2]]] &]
Select[Partition[Range[1, 23518000, 2], 4, 1], AllTrue[ FromDigits[ #]&/@ IntegerDigits[#, 2], PrimeQ]&][[All, 1]] (* Harvey P. Dale, Aug 30 2021 *)

Prog

(PARI) has(n)=isprime(fromdigits(binary(n), 10))
is(n)=has(n) && has(n+2) && has(n+4) && has(n+6) \\ Charles R Greathouse IV, Jan 29 2017

Crossrefs

Cf. A000040, A007088, A036952.

Sequence in context: A251117 A076814 A204792 * A147314 A209813 A034632

Adjacent sequences: A281618 A281619 A281620 * A281622 A281623 A281624

Keyword

nonn,base

Author

K. D. Bajpai, Jan 25 2017

Status

approved