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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
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
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.
MATHEMATICA
Select[Prime[Range[1250]], Mod[ # - 1, 9] + 1 ==Mod[NextPrime[#]-1, 9]+1&] (* James C. McMahon, Sep 14 2024 *)
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
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