A175590 Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).

19940, 49147, 54585, 118923, 136825, 183554, 204323, 204324, 262932, 304675, 361275, 361322, 476377, 486962, 506905, 619722, 668211, 734948, 854018, 937025, 938203, 999649, 1062025, 1118275, 1335572, 1336075, 1356324, 1466225, 1541491

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1) = 2^2 * 5 * 997; a(1)+1 = 3 * 17^2 * 23; a(1)+2 = 2 * 13^2 * 59; a(1)+3 = 7^2 * 11 * 37. All have prime signature {2, 1, 1}.

Mathematica

SequencePosition[Table[Sort[FactorInteger[n][[All, 2]]], {n, 1542000}], {x_, x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *0 (* Harvey P. Dale, Jun 09 2021 *)

Prog

(PARI) sig(n)={vecsort(factor(n)[, 2])}; s=sig(1); for(n=1, 1e6, t=sig(n+1); if(s==t&t==sig(n+2)&t==sig(n+3), print1(n-1, ", ")); s=t)
(PARI) is_A175590(n)={my(f(n)=vecsort(factor(n)[, 2]), t=f(n)); !for(i=1, 3, f(n+i)!=t & return)}  \\ - M. F. Hasler, Nov 01 2012

Crossrefs

Cf. A052213, A052214, A218448. Subsequence of A070284.

Sequence in context: A263298 A237564 A171353 * A324594 A203045 A307474

Adjacent sequences: A175587 A175588 A175589 * A175591 A175592 A175593

Keyword

nonn

Author

Charles R Greathouse IV, Jul 19 2010

Status

approved