A265113 Primes p such that p and p^2 have the same number of 1's in their binary representations.

2, 3, 7, 31, 79, 127, 157, 317, 379, 751, 1087, 1151, 1277, 1279, 1531, 1789, 1951, 2297, 2557, 2927, 3067, 3259, 3319, 3581, 4253, 4349, 5119, 5231, 5503, 5807, 5821, 6271, 6653, 6871, 8191, 8447, 8689, 9209, 10079, 10837, 11597, 11903, 12799, 13309, 13591

Offset

1,1

Comments

Primes p such that p^2 is in A089042.

Primes p such that A000120(p) = A000120(p^2).

Contains all terms > 43 in A079361.

Subset of A077436.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

7 is in the sequence because 7 and 7^2 = 49 have binary representations 111 and 110001 which both have three 1's.

Maple

f:= proc(n) isprime(n) and (convert(convert(n, base, 2), `+`) = convert(convert(n^2, base, 2), `+`)) end proc:
select(f, [2, seq(i, i=3..10^5, 2)]);

Mathematica

Select[ Prime@ Range@ 1700, DigitCount[n, 2, 1] == DigitCount[n^2, 2, 1],  &] (* Robert G. Wilson v, Dec 01 2015 *)

Prog

(Magma) [NthPrime(n): n in [1..2000] | Multiplicity({* z: z in Intseq(NthPrime(n)^2, 2) *}, 1) eq &+Intseq(NthPrime(n), 2)]; // Vincenzo Librandi, Dec 02 2015
(PARI) c(k, d, b) = {my(c=0, f); while (k>b-1, f=k-b*(k\b); if (f==d, c++); k\=b); if (k==d, c++); return(c)}
forprime(p=2, 1e5, if(c(p, 1, 2) == c(p^2, 1, 2), print1(p, ", "))) \\ Altug Alkan, Dec 02 2015

Crossrefs

Cf. A000120, A077436, A079361, A089042.

Sequence in context: A268477 A156313 A163075 * A228171 A089359 A239892

Adjacent sequences: A265110 A265111 A265112 * A265114 A265115 A265116

Keyword

nonn,base

Author

Robert Israel, Dec 01 2015

Status

approved