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
Examples
7 is in the sequence because 7 and 7^2 = 49 have binary representations 111 and 110001 which both have three 1's.
Links
- Robert Israel, Table of n, a(n) for n = 1..1000
Programs
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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 -
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)]);
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Mathematica
Select[ Prime@ Range@ 1700, DigitCount[n, 2, 1] == DigitCount[n^2, 2, 1], &] (* Robert G. Wilson v, Dec 01 2015 *)
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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
Comments