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Search: id:A080188
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| A080188 |
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Primes p such that 13 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248). |
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2
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| 23, 311, 349, 857, 1091, 1871, 1949, 2027, 2339, 2729, 3119, 3821, 5849, 6551, 7487, 9437, 10139, 10529, 11699, 15287, 18251, 21059, 21839, 38609, 42899, 49919, 51479, 57329, 61151, 65519, 69497, 70199, 70979, 81899, 97499, 108107, 109199, 114659
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence appears to consist of 23, 349 and the lesser of twin primes q (A001359) such that q+1 is 13-smooth (A080197) but not 11-smooth (A051038, A080196).
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EXAMPLE
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349 is a term since 350 = 2*5^2*7, 351 = 3^3*13, 352 = 2^5*11 are the numbers between 349 and the next prime 353; 857 is a term since 858 = 2*3*11*13 is the only number between 857 and the next prime 859.
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PROGRAM
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(PARI) {forprime(p=2, 120000, q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=13, f=factor(j); a=f[matsize(f)[1], 1]; if(m<a, m=a); j++); if(m==13, print1(p, ", ")))}
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CROSSREFS
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Cf. A052248, A001359, A080197, A051038, A080196.
Sequence in context: A077203 A090927 A045530 this_sequence A142433 A125458 A022747
Adjacent sequences: A080185 A080186 A080187 this_sequence A080189 A080190 A080191
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 10 2003
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