A104421 Numbers n such that n, prime(n), prime(n)+n, prime(n)-n and prime(n)*n all numbers without the digit 1.

74, 75, 80, 86, 87, 95, 96, 350, 352, 354, 355, 357, 360, 364, 376, 536, 557, 564, 583, 584, 590, 592, 593, 594, 596, 599, 600, 623, 635, 639, 656, 659, 660, 665, 667, 674, 677, 678, 699, 700, 703, 706, 707, 724, 728, 734, 744, 750, 759, 762, 765, 766, 770

Offset: 1

Author

Zak Seidov, Mar 07 2005

Keywords

• nonn
• base
• changed

Comments

The graph is of quasi-piecewise linear character.

Any other reasonable function(s) of p and m not having digit 1?

Subsequence of A084368: a(1) = 75 = A084368(36), a(100) = 2744 = A084368(898). - Zak Seidov, Dec 04 2013

Examples

			For n = 74, p = prime(74) = 373, p + n = 447, p - n = 299, p*n = 27602.
For n = 256709, p = prime(256709) = 3599737, p + n = 3856446, p - n = 3343028, p*n = 924084885533.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A038603, A084368, A104419-A104428.

Programs

Mathematica

id[x_]:=IntegerDigits[x]; pr[i_]:=Prime[i]; ra=Range[3000]; A104421=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 1]=={}&]
prQ[n_]:=With[{p=Prime[n]},AllTrue[IntegerDigits/@{n,p,p+n,p-n,p*n},FreeQ[#,1]&]]; Select[Range[1000],prQ] (* Harvey P. Dale, Aug 29 2025 *)