A231965 Smallest integer starting a group of exactly n consecutive untouchable numbers (A005114) with term differences of 2.

246, 288, 892, 9020, 11456, 23480, 52274, 33686, 190070, 1741856, 1668564, 7806762

Offset: 2

Author

Michel Marcus, Nov 16 2013

Keywords

• nonn
• more

Comments

Such n-tuplets from A005114 correspond to n+1 positive numbers interspersed with n zeros in A070015, and starting at a(n) - 1. For instance, a(4) = 892 is related to A070015(891) and consecutive values: 2661, 0, 4147, 0, 2945, 0, 1287, 0, 9757.

Examples

			a(5) = 9020, because 9020, 9022, 9024, 9026, 9028 are untouchable, while 9018 and 9030 are not so (A001065). For examples with smaller n, see A231964 comments.
		

Links

• Eric Weisstein's World of Mathematics, Untouchable Number.
• Wikipedia, Untouchable number

Crossrefs

Cf. A001065, A005114, A231964.

Cf. A110875 (analog for sigma(n)).

Programs

PARI

oksucc(v, vi, n) = {for (i = 1, n-1, if (! vecsearch(v, vi+2*i, ) , return (0));); return(! vecsearch(v, vi-2) && !vecsearch(v, vi+2*n));}
a(n) = {v = readvec("untouchable.log"); for (i=1, #v, vi = v[i]; if (oksucc(v, vi, n), return(vi)););} \\ readvec reads the file obtained by keeping the second column of b005114.txt seen as a csv file.

Extensions

a(10)-a(13) from Donovan Johnson, Nov 16 2013

Definition, data, and Pari script corrected by Michel Marcus with Donovan Johnson, Nov 18 2013