A082555 -id:A082555 - cp's OEIS frontend

A073779 Number of 0's in base-3 representation of n-th prime.

0, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 3, 2, 1, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 0, 0, 3, 2, 2, 1, 2, 2, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 3, 2, 3, 2, 3, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 0, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 1, 4, 3, 2, 2, 2, 2, 2, 3, 2, 1, 1, 3, 2

Offset: 1

Zak Seidov, Aug 11 2002

a(n) = 0 if prime(n) is in A082555. - Robert Israel, Dec 28 2018

			a(10)=2 as 10th prime is 29 in base-10 representation, or 1002 in base-3 representation.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A073780, A073781, A077267, A082555.

[ Multiplicity({* a: a in Intseq(p, 3) *}, 0): p in PrimesUpTo(600) ]; // Klaus Brockhaus, Oct 10 2010

f:= n -> numboccur(0,convert(ithprime(n),base,3)):
map(f, [$1..200]); # Robert Israel, Dec 28 2018

A073779[n_] := Length[Cases[IntegerDigits[Prime[n], 3], 0]];
DigitCount[#,3,0]&/@Prime[Range[120]]  (* Harvey P. Dale, Apr 26 2011 *)

a(n) = A077267(A000040(n)). - Michel Marcus, Oct 02 2013

More terms from Klaus Brockhaus, Oct 10 2010

A181172 Primes whose base 4 representation does not contain a 0.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 89, 101, 103, 107, 109, 127, 149, 151, 157, 167, 173, 181, 191, 223, 229, 233, 239, 251, 347, 349, 359, 367, 373, 379, 383, 409, 421, 431, 439, 443, 479, 487, 491, 503, 509, 599, 601, 607, 613, 617, 619

Offset: 1

Jonathan D. B. Hodgson, Oct 08 2010

This sequence contains all Mersenne primes (i.e. this is a supersequence of A000668). - Iain Fox, Dec 25 2017

			53 = 311 (base 4), which contains no 0.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A082555, A000668 (subsequence).

Cf. A073779 (number of 0's in base-3 representation of n-th prime), A181173 (primes whose base 5 representation does not contain a 0). - Klaus Brockhaus, Oct 10 2010

[ p: p in PrimesUpTo(620) | not exists(t){d: d in Intseq(p, 4) | d eq 0 } ]; // Klaus Brockhaus, Oct 10 2010

The following code will store the first 200 terms into a sequence K. for i from 1 to 200 do if i=i then x[i]:=convert(ithprime(i),base,4) else x[i]:=0 end if: end do: S:={}: for i from 1 to 200 do if evalb(`in`(0, x[i]))=false then S:=S union {i} fi od; for i from 1 to nops(S)do z[i]:=ithprime(S[i]) od: K:=[seq((z[i]),i=1..nops(S))];
# Alternative:
select(t -> isprime(t) and not has(convert(t,base,4),0), [2,seq(i,i=3..10^4,2)]); # Robert Israel, Dec 24 2017

Select[Prime@ Range@ 120, DigitCount[#, 4, 0] == 0 &] (* Michael De Vlieger, Dec 24 2017 *)

lista(nn) = forprime(p=2, nn, if(!setsearch(Set(digits(p, 4)), 0), print1(p, ", "))) \\ Iain Fox, Dec 25 2017

A181173 Primes whose base 5 representation does not contain a 0.

Original entry on oeis.org

2, 3, 7, 11, 13, 17, 19, 23, 31, 37, 41, 43, 47, 59, 61, 67, 71, 73, 83, 89, 97, 107, 109, 113, 157, 163, 167, 173, 181, 191, 193, 197, 199, 211, 223, 233, 239, 241, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 359, 367, 373, 409, 419, 421, 431, 433

Offset: 1

Jonathan D. B. Hodgson, Oct 08 2010

			23 = 43 (base 5) which contains no 0.

Cf. A082555.

The following stores the first 200 digits of the sequence in K: for i from 1 to 200 do if i=i then x[i]:=convert(ithprime(i),base,5) else x[i]:=0 end if: end do: S:={}: for i from 1 to 200 do if evalb(`in`(0, x[i]))=false then S:=S union {i} fi od; for i from 1 to nops(S)do z[i]:=ithprime(S[i]) od: K:=[seq((z[i]),i=1..nops(S))];

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A073779 Number of 0's in base-3 representation of n-th prime.

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A181172 Primes whose base 4 representation does not contain a 0.

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A181173 Primes whose base 5 representation does not contain a 0.

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