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A129809 Lesser of consecutive prime pairs whose last digits differ by 2. 1

%I #16 Sep 14 2018 12:41:04

%S 3,5,11,17,41,71,89,101,107,137,191,197,211,227,281,311,347,359,389,

%T 431,449,461,467,479,521,523,617,641,661,683,719,743,797,821,827,857,

%U 881,929,983,997

%N Lesser of consecutive prime pairs whose last digits differ by 2.

%C Conjecture: The number of terms in this sequence is infinite.

%C This follows from Dickson's conjecture. - _Charles R Greathouse IV_, Jan 29 2013

%H Charles R Greathouse IV, <a href="/A129809/b129809.txt">Table of n, a(n) for n = 1..10000</a>

%F I conjecture that a(n) ~ 4n log n. - _Charles R Greathouse IV_, Jan 29 2013

%e The last digits of the consecutive prime pair 89 and 97 differ by 2 so 89 is in the table.

%t Select[Partition[Prime[Range[200]],2,1],Abs[Mod[#[[1]],10]-Mod[#[[2]],10]] == 2&][[All,1]] (* _Harvey P. Dale_, Sep 14 2018 *)

%o (PARI) \d can be 2,4,6,8 primediffd(n,d) = { forprime(x=3,n, y=abs((nextprime(x+1)%10-x%10)); if(y==d,print1(x",") ) ) }

%o (PARI) p=2;forprime(q=3,1e4,if(abs(q%10-p%10)==2,print1(p", "));p=q) \\ _Charles R Greathouse IV_, Jan 29 2013

%K easy,nonn,base

%O 1,1

%A _Cino Hilliard_, May 19 2007

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)