A077658 Least composite number not congruent to 0 (modulo the first n primes) which contains its greatest proper divisor as a substring of itself, both in base two.

4, 55, 55, 91, 407, 493, 493, 893, 1189, 1189, 1643, 1681, 1681, 7597, 7597, 7597, 7597, 7597, 7597, 7597, 7979, 7979, 9167, 9167, 11227, 11227, 11227, 28757, 28757, 28757, 28757, 28757, 28757, 28757, 28757, 36349, 36349, 36349, 39917, 39917

Offset

0,1

Links

Table of n, a(n) for n=0..39.

Example

a(0)=4 since 4_d = 100_b and its largest proper divisor is 2_d = 10_b is a substring and 4 is not prime. a(2) = 55 since 55_d = 110111_b and its largest proper divisor is 11_d = 1011_b is a substring and 55 is not prime nor congruent to 0 (modulo either 2 or 3). a(4) = 407 since 407_d = 110010111_b and its largest proper divisor is 37_d = 100101_b is a substring and 407 is not prime nor congruent to 0 (modulo either 2, 3, 5, or 7).

Mathematica

a = {}; k = 1; Do[p = Table[ Prime[i], {i, 1, n}]; While[ PrimeQ[k] || Sort[Mod[k, p]] [[1]] == 0 || StringPosition[ ToString[ FromDigits[ IntegerDigits[k, 2]]], ToString[ FromDigits[ IntegerDigits[ Divisors[k] [[ -2]], 2]] ]] == {}, k++ ]; a = Append[a, k], {n, 0, 100}]; a

Crossrefs

Cf. A063138.

Sequence in context: A361524 A140604 A048371 * A217124 A064439 A352510

Adjacent sequences: A077655 A077656 A077657 * A077659 A077660 A077661

Keyword

base,nonn

Author

Robert G. Wilson v, Nov 13 2002

Status

approved