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Search: id:A117838
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| A117838 |
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Smaller of two consecutive prime numbers with the same digital root. |
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+0
2
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| 523, 1069, 1259, 1381, 1759, 1913, 2161, 2503, 2861, 3803, 3889, 4159, 4373, 4423, 4463, 4603, 4703, 4733, 5059, 5209, 5483, 6011, 6229, 6451, 6529, 6581, 6619, 7159, 7351, 7393, 7433, 7459, 7621, 7883, 8191, 8761, 9109, 9293, 9551, 9749, 9949
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Contains all sequences with primes that are followed by a prime gap which is a multiple of 18 - since adding multiples of 9 does not change the digital root and the gaps are even. So A031936 (gap 18) and A134117 (gap 36) are subsequences and lower primes of prime gap 54 (35617, 40289, 40639, 86869, 100853,...), prime gap 72 (31397, 360091, 507217, 517639, 633667, 650107, 705317....) or prime gap 90 (404851,576791,..), for example, are also in here (cf. A000230). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 14 2008
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LINKS
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M. F. Hasler, Table of n, a(n) for n=1,...,5833.
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FORMULA
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{A000040(i): 18 | A001223(i), any i}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 14 2008
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EXAMPLE
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523 and 541 are two consecutive prime numbers with the same digital root, namely 1.
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PROGRAM
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(PARI from M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 13 2008) isA117838(p)={ (nextprime(p+1)-p)%9==0 }
forprime( p=1, 10^4, isA117838(p) & print1(p", "))
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CROSSREFS
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Sequence in context: A152673 A124587 A095651 this_sequence A031936 A066540 A080912
Adjacent sequences: A117835 A117836 A117837 this_sequence A117839 A117840 A117841
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006
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EXTENSIONS
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Corrected by R. J. Mathar and M. F. Hasler, Apr 13 2008
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