%I #15 Jul 25 2024 08:50:15
%S 4357,6301,6553,7741,8011,12277,13339,14437,14923,16273,18307,24733,
%T 26731,27091,34471,34543,35227,36217,36307,36433,36523,37783,41491,
%U 41851,41941,42373,43543,45181,47017,49411,52543,53407,54217,55207,57943,58321,58411,64513
%N Honaker primes of the form p = 2*k-1 with sum-of-digits(p) = sum-of-digits(k).
%C The set of Honaker primes A033548 is intersected with the set {37, 73, 109, 127, 163, 181, 271, 307, 397, 433, 523, 541, 577, 613,...} of primes p = 2k-1, where A007953(p) = A007953(k) for the digit sums.
%C The requirement on the digit sum defining the Honaker primes plus the additional requirement on the digits sum of k means both digit sums are of the form 9*m+1, m>=1.
%C The sequence contains prime(n) for n = 595, 820, 847, 982, 1009, 1099, 1468, 15856, 1693, 1747,...
%C The fourth to sixth member of the sequence are three consecutive Honaker primes.
%C As a curiosity we have that for p=120709 = prime(11359) = A033548(469), k=60355 even the index in the Honaker primes has the same sum, 19.
%D M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Beck, 4. Auflage, 2005
%e p = 2719 = prime(397) has digit sum 19, but k = 1360 has digit sum 10, which yields no term.
%e p = 6301 = prime(820) with k = 3151, digit sum 10, is the 2nd term.
%e p = 10711 = prime(1306) with digit sum 10, but k = 5356 has digit sum 10: no contribution to the sequence.
%e p = 57943 = prime(5869) with k = 28972 have common digit sum 28 and p is in the sequence.
%Y Cf. A000040, A033548, A176012
%K base,nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 08 2010
%E 4137 replaced by 4357, 8821 removed, Extensive list of auxiliary prime indices reduced - _R. J. Mathar_, Nov 01 2010