A306217 Sphenic numbers with a prime nearest neighbor.

30, 42, 66, 70, 78, 102, 110, 114, 130, 138, 174, 182, 190, 222, 230, 238, 258, 282, 310, 318, 354, 366, 374, 402, 410, 418, 430, 434, 438, 442, 498, 598, 602, 606, 618, 642, 646, 654, 658, 678, 682, 710, 742, 762, 786, 822, 826, 830, 854, 906, 938, 942, 946, 970, 978

Offset

1,1

Comments

Terms are of the form 4k + 2.

Links

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

Example

30 is a term because (2*3*5) - 1 = 29 and (2*3*5) + 1 = 31.
42 is a term because (2*3*7) - 1 = 41 and (2*3*7) + 1 = 43.
66 is a term because (2*3*11) + 1 = 67.
70 is a term because (2*5*7) + 1 = 71.

Maple

Res:= NULL: count:= 0: last:= 0: p:= 3;
while count < 100 do
  p:= nextprime(p);
  if p mod 4 = 3 then
    if p-1 <> last then
      F:= ifactors(p-1)[2];
      if nops(F) = 3 and {F[1, 2], F[2, 2], F[3, 2]}={1} then
        Res:= Res, p-1;
        count:= count+1;
    fi fi
  else
    F:= ifactors(p+1)[2];
    last:= p+1;
    if nops(F) = 3 and {F[1, 2], F[2, 2], F[3, 2]}={1} then
       Res:= Res, p+1;
       count:= count+1;
    fi
  fi
od:
Res; # Robert Israel, Feb 17 2019

Mathematica

Select[Range[2, 10^3, 4], And[AnyTrue[# + {-1, 1}, PrimeQ], SquareFreeQ@ #, PrimeNu@ # == 3] &] (* Michael De Vlieger, Jan 29 2019 *)

Prog

(PARI) lista(nn) = for(n=1, nn, if(bigomega(n)==3 && omega(n)==3 && (isprime(n-1) || isprime(n+1)), print1(n", "))); \\ Michel Marcus, Jan 30 2019

Crossrefs

Cf. A007304, A000040.

Subsequence of A016825.

Sequence in context: A160350 A053858 A075819 * A034683 A328328 A302574

Adjacent sequences: A306214 A306215 A306216 * A306218 A306219 A306220

Keyword

nonn

Author

Torlach Rush, Jan 29 2019

Extensions

Corrected and extended by Michel Marcus, Jan 30 2019

Status

approved