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Search: id:A077658
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| A077658 |
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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. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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0,1
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EXAMPLE
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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).
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MATHEMATICA
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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
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CROSSREFS
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Cf. A063138.
Sequence in context: A107101 A140604 A048371 this_sequence A064439 A133218 A073352
Adjacent sequences: A077655 A077656 A077657 this_sequence A077659 A077660 A077661
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KEYWORD
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base,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 13 2002
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