A176111 Honaker primes of the form p = 2*k-1 with sum-of-digits(p) = sum-of-digits(k).

4357, 6301, 6553, 7741, 8011, 12277, 13339, 14437, 14923, 16273, 18307, 24733, 26731, 27091, 34471, 34543, 35227, 36217, 36307, 36433, 36523, 37783, 41491, 41851, 41941, 42373, 43543, 45181, 47017, 49411, 52543, 53407, 54217, 55207, 57943, 58321, 58411, 64513

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 08 2010

Keywords

• base
• nonn

Comments

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.

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.

The sequence contains prime(n) for n = 595, 820, 847, 982, 1009, 1099, 1468, 15856, 1693, 1747,...

The fourth to sixth member of the sequence are three consecutive Honaker primes.

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.

Examples

			p = 2719 = prime(397) has digit sum 19, but k = 1360 has digit sum 10, which yields no term.
p = 6301 = prime(820) with k = 3151, digit sum 10, is the 2nd term.
p = 10711 = prime(1306) with digit sum 10, but k = 5356 has digit sum 10: no contribution to the sequence.
p = 57943 = prime(5869) with k = 28972 have common digit sum 28 and p is in the sequence.
		

References

• M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Beck, 4. Auflage, 2005

Crossrefs

Cf. A000040, A033548, A176012

Extensions

4137 replaced by 4357, 8821 removed, Extensive list of auxiliary prime indices reduced - R. J. Mathar, Nov 01 2010