

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
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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



