A108343 Gapful numbers >= 100: numbers that are divisible by the number formed by their first and last digit. Numbers up to 100 trivially have this property and are excluded.

100, 105, 108, 110, 120, 121, 130, 132, 135, 140, 143, 150, 154, 160, 165, 170, 176, 180, 187, 190, 192, 195, 198, 200, 220, 225, 231, 240, 242, 253, 260, 264, 275, 280, 286, 297, 300, 315, 330, 341, 352, 360, 363, 374, 385, 390, 396, 400, 405, 440, 451

Offset

1,1

Links

Aaron Toponce, Table of n, a(n) for n = 1..10000

Formula

For n > 10, 6n < a(n) < 14n. - Charles R Greathouse IV, Oct 15 2025

a(n+1) <= a(n) + 90. Infinitely often a(n+10) = a(n) + 10. a(n+11) > a(n) + 11. - Charles R Greathouse IV, Oct 15 2025

Example

253 is in the sequence because 253 = 11 * 23 and 23 is the concatenation of 2 and 3 (first and last digit of 253).

Mathematica

fQ[ n_ ] := Block[ {id = IntegerDigits[ n ]}, IntegerQ[ n / FromDigits[ {id[ [ 1 ] ], id[ [ -1 ] ]} ] ] ]; Select[ Range[ 100, 461 ], fQ[ # ] & ] (* Robert G. Wilson v, Jul 19 2005 *)

Prog

(PARI) is(n)=n>99 && n%(n\10^logint(n, 10)*10+n%10)==0 \\ Charles R Greathouse IV, Oct 15 2025

Crossrefs

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Sequence in context: A092633 A213313 A204584 * A349771 A343552 A204585

Adjacent sequences: A108340 A108341 A108342 * A108344 A108345 A108346

Keyword

nonn,base,easy

Author

Luca Colucci, Jul 01 2005

Extensions

Corrected and extended by Robert G. Wilson v, Jul 19 2005

Status

approved