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

1,1

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.

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

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