OFFSET
1,1
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..10000
Fred B. Holt, On the last digits of consecutive primes, arXiv:1604.02443 [math.NT], 2016.
Robert J. Lemke Oliver, Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv:1603.03720 [math.NT], 2016.
FORMULA
Numbers n such that A000040(n)==A000040(n+1) mod 10, or A000040(n+1) - A000040(n) = 10*k for some integer k, or n such that A129750(n) = 0. [Corrected and edited by M. F. Hasler, Oct 24 2018]
EXAMPLE
a(1) = 34 because prime(34) = 139, prime(35) = 149, both end with the digit 9.
a(2) = 42 because prime(42) = 181, prime(43) = 191, both end with the digit 1.
a(4) = 61 because prime(61) = 283, prime(62) = 293, both end with the digit 3.
a(5) = 68 because prime(68) = 337, prime(69) = 347, both end with the digit 7.
MAPLE
isA107730 := proc(n) local ldign, ldign2 ; ldign := convert(ithprime(n), base, 10) ; ldign2 := convert(ithprime(n+1), base, 10) ; if op(1, ldign) = op(1, ldign2) then true ; else false ; fi ; end: for n from 1 to 600 do if isA107730(n) then printf("%d, ", n) ; fi ; od ; # R. J. Mathar, Jun 15 2007
MATHEMATICA
Select[Range[200], IntegerDigits[Prime[ # ]][[ -1]]==IntegerDigits[Prime[ #+1]][[ -1]]&] (* Stefan Steinerberger, Jun 14 2007 *)
Flatten[Position[Partition[Prime[Range[600]], 2, 1], _?(Mod[#[[1]], 10] == Mod[#[[2]], 10]&), {1}, Heads->False]] (* Harvey P. Dale, Aug 20 2015 *)
PROG
(PARI) isok(n) = (prime(n) % 10) == prime(n+1) % 10; \\ Michel Marcus, Feb 16 2017
(PARI) is_A107730(n)=!((nextprime(1+n=prime(n))-n)%10) \\ This (...) is twice as fast as prime(n+1)-prime(n), and prime(n) becomes very slow for n > 41538, even with primelimit = 10^7. - M. F. Hasler, Oct 24 2018
(GAP) P:=List(Filtered([1..4000], IsPrime), n->Reversed(ListOfDigits(n)));;
a:=Filtered([1..Length(P)-1], i->P[i+1][1]=P[i][1]); # Muniru A Asiru, Oct 31 2018
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Jun 12 2007
EXTENSIONS
More terms from Stefan Steinerberger and R. J. Mathar, Jun 14 2007
STATUS
approved