A063163 Composite numbers which in base 7 contain their largest proper factor as a substring.

49, 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 343, 371, 413, 427, 469, 497, 511, 539, 551, 553, 581, 623, 637, 679, 707, 721, 749, 763, 791, 833, 847, 889, 917, 931, 959, 973, 989, 1001, 1043, 1057, 1099, 1127, 1141, 1169, 1183, 1211, 1253

Offset: 1

Author

Robert G. Wilson v, Aug 08 2001

Keywords

• base
• nonn

Comments

Sequence contains every term of A084968 except 7. - Bill McEachen, Dec 29 2020

Examples

			91 = 160_7 and its largest proper factor is 13 = 16_7 where 16 is a substring of 160. - _Bill McEachen_, Dec 30 2020
		

Links

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

Crossrefs

Cf. A062238, A032742, A084968.

Programs

Mathematica

Do[ If[ !PrimeQ[ n ] && StringPosition[ ToString[ FromDigits[ IntegerDigits[ n, 7 ] ] ], ToString[ FromDigits[ IntegerDigits[ Divisors[ n ] [ [ -2 ] ], 7 ] ] ] ] != {}, Print[ n ] ], {n, 2, 2000} ]
Select[Range[1300],CompositeQ[#]&&SequenceCount[IntegerDigits[#,7],IntegerDigits[ Divisors[#][[-2]],7]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 21 2021 *)

PARI

isok(n)={mystr=digits(n,7);d=divisors(n);gpf=d[#d-1];seek=digits(gpf,7);ls=#seek;for(w=1,#mystr-ls+1,if(mystr[w]!=seek[1],next);for(h=1,ls-1,if(mystr[w+h]!=seek[h+1],break);if(h==ls-1,return(1))));return(0);} \\ Bill McEachen, Dec 31 2020