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 A117838 Smaller of two consecutive prime numbers with the same digital root. 2

%I

%S 523,1069,1259,1381,1759,1913,2161,2503,2861,3803,3889,4159,4373,4423,

%T 4463,4603,4703,4733,5059,5209,5483,6011,6229,6451,6529,6581,6619,

%U 7159,7351,7393,7433,7459,7621,7883,8191,8761,9109,9293,9551,9749,9949

%N Smaller of two consecutive prime numbers with the same digital root.

%C 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

%H M. F. Hasler, <a href="/A117838/b117838.txt">Table of n, a(n) for n = 1..5833</a>.

%F {A000040(i): 18 | A001223(i), any i}. - _R. J. Mathar_, Apr 14 2008

%e 523 and 541 are two consecutive prime numbers with the same digital root, namely 1.

%o (PARI) isA117838(p)={ (nextprime(p+1)-p)%9==0 }

%o forprime( p=1,10^4, isA117838(p) & print1(p", ")) \\ _M. F. Hasler_, Apr 13 2008

%K base,nonn

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006

%E Corrected by _R. J. Mathar_ and _M. F. Hasler_, Apr 13 2008

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)