cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A178350 Semiprimes with both a prime number of 0's and a prime number of 1's in their binary representations.

Original entry on oeis.org

9, 10, 21, 22, 25, 26, 35, 38, 49, 65, 87, 91, 93, 94, 115, 118, 121, 122, 133, 134, 143, 145, 146, 155, 158, 161, 185, 194, 203, 205, 206, 213, 214, 217, 218, 319, 381, 382, 415, 445, 446, 471, 478, 493, 501, 502, 505, 515, 517, 527, 529, 535, 542, 545, 551
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 25 2010

Keywords

Examples

			a(1)=9 because 9(written in base 10)=1001 where 2=prime number of 0's and 2=prime number of 1's.
		

Crossrefs

Programs

  • Maple
    A000120 := proc(n) add(d,d=convert(n,base,2)) ; end proc:
    A080791 := proc(n) dgs :=convert(n,base,2) ; nops(dgs)-A000120(n) ; end proc:
    for n from 1 to 300 do spr :=A001358(n) ; if isprime( A080791(spr) ) and isprime(A000120(spr)) then printf("%d,",spr) ; end if; end do: # R. J. Mathar, Aug 12 2010
  • Mathematica
    Select[Range[600],PrimeOmega[#]==2&&AllTrue[{DigitCount[ #,2,0], DigitCount[ #,2,1]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 25 2016 *)

Extensions

Corrected (167 removed) by R. J. Mathar, Aug 12 2010

A169817 n-th prime with both a prime number of 0's and a prime number of 1's in binary representation minus n-th semiprime with both a prime number of 0's and a prime number of 1's in their binary representation.

Original entry on oeis.org

8, 9, 16, 19, 54, 77, 72, 71, 82, 72, 64, 66, 74, 79, 64, 63, 72, 77, 78, 93, 86, 88, 95, 102, 209, 218, 246, 245, 240, 258, 281, 278, 285, 304, 323, 238, 182, 187, 162, 142, 155, 136, 135, 124, 130, 139, 142, 138, 142, 134, 148, 166, 167, 174, 176, 168, 177, 174
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 25 2010

Keywords

Examples

			a(1)=A144214(1)-A178350(1)=17-9=8.
		

Crossrefs

Programs

  • Mathematica
    pn0Q[n_]:=PrimeQ[DigitCount[n,2,1]]&&PrimeQ[DigitCount[n,2,0]]; nn=600;Module[{ps=Select[Prime[Range[nn]],pn0Q],sps=Select[Range[nn], PrimeOmega[#]==2&&pn0Q[#]&],minlen},minlen=Min[Length[ps], Length[ sps]];First[#]-Last[#]&/@Thread[{Take[ps,minlen],Take[sps,minlen]}]] (* Harvey P. Dale, May 07 2012 *)

Formula

a(n)=A144214(n)-A178350(n).

Extensions

Corrected (96 replaced by 86, all numbers from a(27) on replaced) by R. J. Mathar, Jun 04 2010
Showing 1-2 of 2 results.