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

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

Author

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

Keywords

• base
• nonn

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

Examples

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

Links

• M. F. Hasler, Table of n, a(n) for n = 1..5833.

Programs

Mathematica

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

PARI

isA117838(p)={ (nextprime(p+1)-p)%9==0 }
forprime( p=1,10^4, isA117838(p) & print1(p", ")) \\ M. F. Hasler, Apr 13 2008

Formula

{A000040(i): 18 | A001223(i), any i}. - R. J. Mathar, Apr 14 2008

Extensions

Corrected by R. J. Mathar and M. F. Hasler, Apr 13 2008