A104422 Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 2-less.

5, 6, 16, 18, 30, 36, 78, 81, 83, 90, 94, 95, 100, 103, 104, 105, 108, 110, 111, 114, 131, 133, 136, 137, 139, 153, 154, 159, 160, 166, 488, 489, 495, 496, 498, 499, 500, 510, 511, 514, 640, 641, 643, 644, 645, 646, 650, 665, 669, 671, 680, 685, 687, 688, 690

Offset: 1

Author

Zak Seidov, Mar 07 2005

Keywords

• nonn
• base

Comments

From the first 3000 primes, only 182 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 2-less.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A104419-A104428.

Programs

Mathematica

id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104422=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 2]=={}&]
tlQ[n_]:=DigitCount[n,10,2]==0; Select[Range[700],AllTrue[{#,p=Prime[#], p+#,p-#,p*#},tlQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 09 2018 *)