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

1,1

Comments

The set of Honaker primes A033584 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) = A033584(469), k=60355 even the index in the Honaker primes has the same sum, 19.

References

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

Links

Table of n, a(n) for n=1..38.

Example

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.

Crossrefs

Cf. A000040, A033548, A176012

Sequence in context: A285040 A203928 A340457 * A164517 A125825 A031564

Adjacent sequences: A176108 A176109 A176110 * A176112 A176113 A176114

Keyword

base,nonn

Author

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

Extensions

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

Status

approved