login
Start of a run of consecutive primes of length n each ending with the same digit.
8

%I #24 Nov 16 2019 15:42:15

%S 2,139,1627,18839,123229,776257,3873011,23884639,36539311,196943081,

%T 452942827,73712513057,154351758091,154351758091,4010803176619,

%U 6987191424553,71894236537009,196948379177587,253931039382791

%N Start of a run of consecutive primes of length n each ending with the same digit.

%C n consecutive primes differ by a multiple of 10 starting at a(n).

%C n consecutive primes that are congruent mod 10, i.e., they are not necessarily in arithmetic progression.

%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.

%H William F. Sindelar, Mark Underwood, Mikael Klasson, <a href="/A054681/a054681.txt">Gaps Between Consecutive Odds not Divisible by 3</a>, digest of 5 messages in primenumbers Yahoo group, Jun 27 - Jun 29, 2003. [Cached copy]

%H Mark Underwood's <a href="http://groups.yahoo.com/group/primenumbers/message/12794">Problem posed on the "PrimeNumbers" yahoogroup</a> (2003)

%e a(2)=139 because 139 and 149 are the first consecutive primes to share a terminal digit.

%o (PARI) i=1; s=0; d=0; l=0; forprime(p=1,500000,if(p%10==d,l++,if(l>=i,print(s); i++); s=p; d=p%10; l=1)) \\ (Carmody)

%K nonn,base

%O 1,1

%A _Jeff Burch_, Apr 18 2000

%E More terms from _Phil Carmody_, Jun 27 2003

%E Further from _Jens Kruse Andersen_, Jun 03 2006

%E a(17)-a(19) from _Giovanni Resta_, Aug 01 2013