A133219 Smallest composite integer in base n which remains composite after altering any one or two digits.

1010100, 2200100, 20130000, 3243003420, 55111253530, 5411665056000, 33254100107730, 210324811482600, 977731833235239280

Offset

2,1

Comments

Changing the most significant digit to 0 is allowed. The problem (base 10) was posed by W. Sierpinski, published in 1977. There are an infinite number of solutions if a certain Erdos conjecture on congruences is true. a(2) through a(9) are proved minimal, a(10) has not yet been proved minimal.

Links

Table of n, a(n) for n=2..10.

Witold Jarnicki and Maciej Zenczykowski, On a property of the number 977731833235239280, arXiv:0709.3361 [math.NT], 2007

Example

a(3) base 10 = 1953. a(4) base 10 = 34560. a(5) base 10 = 7000485. a(6) base 10 = 354748446. a(7) base 10 = 77478704205. a(8) base 10 = 1878528135128. a(9) base 10 = 48398467146642.

Crossrefs

Cf. A220289.

Sequence in context: A330519 A066354 A220289 * A306515 A306517 A043643

Adjacent sequences: A133216 A133217 A133218 * A133220 A133221 A133222

Keyword

base,more,nonn

Author

Jonathan Vos Post, Oct 11 2007

Extensions

a(2) and the definition were corrected by Witold Jarnicki, Oct 11 2007

Status

approved