A086887 a(n) = least semiprime with factors not previously used containing integers 2n and 2n+1 as substrings.

1111, 6, 205, 427, 1577, 11639, 1651, 22499, 2771, 34571, 253411, 5129, 60491, 59701, 8149, 9517, 307793, 122491, 13579, 53237, 168019, 18103, 202451, 21667, 169963, 377753, 27613, 301337, 88391, 34633, 368413, 750523, 418573, 44287, 183727, 49771, 53071, 562451, 210797, 62173, 656099, 232343

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

From Robert Israel, Jul 19 2026: (Start)

a(n) = A394347(2*n) * A394347(2*n+1).

This is true if "not previously used" forbids the factor containing 2*n+1 from being the same as the factor containing 2*n. If we allow those factors to be the same, it could happen that they are the same, in which case a(n) < A394347(2*n) * A394347(2*n+1). (End)

Example

Sequence:....1111....6...205...427...1577....11639....1651..
Factors.:..101*11..2*3..41*5..61*7..83*19..103*113..127*13..
2n, 2n+1:.....0,1..2,3...4,5...6,7....8,9....10,11...12,13..
n ......:.......0....1.....2.....3......4........5.......6..

Maple

f:= proc(n) local d, m, m1, i, j, Cands, y;
  d:= 1 + ilog10(n);
  if isprime(n) and not member(n, Used) then return n fi;
  for m from 1 do
    if member(n mod 10, [1, 3, 7, 9]) then Cands:= seq(i*10^d+n, i=10^(m-1)..10^m-1)
    else Cands:= NULL
    fi;
    Cands:= sort([Cands, seq(10^m*n+i, i=1..10^m-1, 2),
             seq(seq(seq(10^(m1+d)*i + 10^m1*n+j, i=10^(m-m1-1)..10^(m-m1)-1), j=1..10^m1-1, 2),
               m1=1..m-1) ]);
    for y in Cands do if ListTools:-BinarySearch(Used, y) = 0 and isprime(y) then return y fi;
  od od;
end proc:
Used:= [101, 11]: R:= 1111:
for n from 1 to 100 do
  v:= f(2*n);
  w:= f(2*n+1);
  R:= R, v*w;
  j:= ListTools:-BinaryPlace(Used, v);
  Used:= [op(Used[1..j]), v, op(Used[j+1..-1])];
  j:= ListTools:-BinaryPlace(Used, w);
  Used:= [op(Used[1..j]), w, op(Used[j+1..-1])];
od:
R; # Robert Israel, Jul 19 2026

Crossrefs

Cf. A394347.

Sequence in context: A287283 A277927 A367814 * A278870 A278898 A278915

Adjacent sequences: A086884 A086885 A086886 * A086888 A086889 A086890

Keyword

base,nonn,changed

Author

Jason Earls, Aug 22 2003

Extensions

More terms from Ray Chandler, Aug 31 2003

More terms from Robert Israel, Jul 19 2026

Status

approved