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%I #7 Nov 15 2024 18:51:53
%S 11,83,1181,7937,9239,10631,12143,28429,66973,75307,79609,206593,
%T 311419,348487,397897,408169,518779,628877,654821,708119,735533,
%U 763457,867281,1030201,1519333,1581449,1623863,1688509,1732763,2012657,2037029
%N Prime numbers that are the sum of consecutive prime numbers with the final digit 1 (primes in A030430).
%C Primes in the partial sums of all primes, starting with 11, that have 1 as their final digit. - _Harvey P. Dale_, Nov 15 2024
%H Harvey P. Dale, <a href="/A129077/b129077.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n)=A030430(1)+A030430(2)+...+A030430(x); a is a prime number.
%e a(2)=83 because 83=A030430(1)+ A030430(2)+A030430(3)=11+31+41 and 83 is a prime number.
%e a(3)=1181 because 1181=A030430(1)+ A030430(2)+A030430(3)+A030430(4)+ A030430(5)+A030430(6)+A030430(7)+ A030430(8)+A030430(9)+A030430(10)+A030430(11)= 11+ 31+ 41+ 61+ 71+ 101+ 131+ 151+ 181+ 191+ 211; and 1181 is a prime number.
%t Select[Accumulate[Select[Prime[Range[2000]],Mod[#,10]==1&]],PrimeQ] (* _Harvey P. Dale_, Nov 15 2024 *)
%Y Cf. A030430; A000040.
%K easy,base,nonn
%O 1,1
%A _Tomas Xordan_, May 11 2007