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A265113 Primes p such that p and p^2 have the same number of 1's in their binary representations. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 05:38 EDT 2020. Contains 336197 sequences. (Running on oeis4.)