A085451 Numbers n such that n and prime[n] together use only distinct digits.

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 17, 19, 20, 21, 24, 25, 27, 28, 35, 39, 40, 45, 53, 57, 58, 60, 61, 69, 70, 72, 79, 85, 89, 90, 91, 93, 96, 98, 104, 108, 120, 124, 145, 146, 147, 150, 162, 236, 237, 253, 254, 259, 315, 316, 359, 380, 384, 390, 405, 406, 460, 461, 518

Offset: 1

Author

Zak Seidov, Jul 01 2003

Keywords

• fini
• full
• nonn
• base

Comments

There are exactly 101 such numbers in the sequence. Numbers with distinct digits in A010784. Primes with distinct digits in A029743. The case n and n^2 (exactly 22 numbers) in A059930.

A178788(A045532(a(n))) = 1. [From Reinhard Zumkeller, Jun 30 2010]

Examples

			3106 is in the sequence (and the last term) because it and prime[3106]=28549 together use all 10 distinct digits.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..101 (full sequence)

Crossrefs

Cf. A010784 A029743 A059930 A085452.

Programs

Mathematica

bb = {}; Do[idpn = IntegerDigits[Prime[n]]; idn = IntegerDigits[n]; If[Length[idn] + Length[idpn] == Length[Union[idn, idpn]], bb = {bb, n}], {n, 1, 100000}]; Flatten[bb]