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.

Showing 1-3 of 3 results.

A073924 Smallest power of 2 that is greater than the previous term such that every partial sum (n>1) is a prime.

Original entry on oeis.org

1, 2, 4, 16, 128, 65536, 9007199254740992, 73786976294838206464, 205688069665150755269371147819668813122841983204197482918576128
Offset: 1

Views

Author

Amarnath Murthy, Aug 19 2002

Keywords

Comments

Next term 2^1752 is too large to include.

Examples

			a(5) is 128 because it is the next power of 2 greater than 16 such that 1 + 2 + 4 + 16 + x is prime.
		

Crossrefs

Cf. A073923.

Programs

  • Mathematica
    a[1] = 1; a[n_] := Block[{k = a[n - 1] + 1, s = Plus @@ (2^Array[a, n - 1])}, While[ !PrimeQ[s + 2^k], k++ ]; k]; Array[2^a[ # ] &, 9] (* Robert G. Wilson v, Jan 31 2006 *)

Extensions

More terms from Jason Earls, Sep 03 2002

A073925 Powers of 2 rearranged such that every partial sum (n>1) is composite.

Original entry on oeis.org

1, 8, 16, 2, 64, 4, 256, 1024, 32, 128, 512, 2048, 8192, 4096, 16384, 32768, 131072, 65536, 2097152, 262144, 524288, 1048576, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 2147483648, 1073741824
Offset: 1

Views

Author

Amarnath Murthy, Aug 19 2002

Keywords

Examples

			a(2)=8 because 1+2=3, 1+4=5 are primes and 1+8=9 is composite.
		

Crossrefs

Programs

  • Maple
    N:= 100: # for terms before the first > 2^N
    Cands:= [seq(2^i,i=0..N)]:
    Res:= NULL: s:= 0: nC:= N+1:
    found:= true;
    while found do
      found:= false;
      for i from 1 to nC do
        if not isprime(s+Cands[i]) then
          Res:= Res, Cands[i];
          s:= s + Cands[i];
          Cands:= subsop(i=NULL, Cands);
          nC:= nC-1;
          found:= true;
          break
        fi
      od
    od:
    Res; # Robert Israel, Apr 05 2020

Extensions

More terms from Sascha Kurz, Feb 01 2003

A073926 Powers of 2 rearranged so that every partial sum after 1 is a proper prime power.

Original entry on oeis.org

1, 8, 16, 2
Offset: 1

Views

Author

Amarnath Murthy, Aug 19 2002

Keywords

Comments

If a(5) exists -- that is, if there is some k for which 2^k + 27 is a proper prime power -- then k > 100000. Or can it be proved that 2^k + 27 is either prime or has more than one distinct prime factor for all k? - Ryan Propper, Jun 17 2006

Crossrefs

Showing 1-3 of 3 results.