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 A117838 Smaller of two consecutive prime numbers with the same digital root. 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, Apr 14 2008 LINKS M. F. Hasler, Table of n, a(n) for n = 1..5833. FORMULA {A000040(i): 18 | A001223(i), any i}. - R. J. Mathar, Apr 14 2008 EXAMPLE 523 and 541 are two consecutive prime numbers with the same digital root, namely 1. PROG (PARI) isA117838(p)={ (nextprime(p+1)-p)%9==0 } forprime( p=1, 10^4, isA117838(p) & print1(p", ")) \\ M. F. Hasler, Apr 13 2008 CROSSREFS Sequence in context: A152673 A124587 A095651 * A031936 A066540 A209875 Adjacent sequences:  A117835 A117836 A117837 * A117839 A117840 A117841 KEYWORD base,nonn AUTHOR Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006 EXTENSIONS Corrected by R. J. Mathar and M. F. Hasler, Apr 13 2008 STATUS approved

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Last modified August 14 03:43 EDT 2020. Contains 336477 sequences. (Running on oeis4.)