A080435 summary and sequences

David Wilson davidwwilson at attbi.com
Mon Apr 14 18:12:10 CEST 2003

Here is a summary of A080435 and related sequences as I computed them.

NJAS: please excuse me for use of A000001 &c.  I am not sure which of these sequences
are already submitted to the OEIS.

Also, Ralf Stephen gives a program for A080435 in a previous post.  You may want to
include it in A080435.

%I A080435
%S A080435 1,2,3,5,7,8,13,14,19,20,23,25,27,31,37,43,47,49,50,55,57,61,67,73,75,79,85,
%T A080435 91,97,98,103,107,109,111,115,121,127,131,133,135,139,140,145,151,157,163,
%U A080435 169,175,181,185,187,193,199,200,205,211,212,217,223,229,235,239,241,245
%N A080435 a(1) = 1; a(n) = least k > a(n-1) such that each prime of form a(i)+a(j) occurs for
unique i <= j.
%K A080435 nonn
%O A080435 1,2
%Y A080435 Cf. A000001, A000002, A000003
%A A080435 Amarnath Murthy (amarnath_murthy at yahoo.com)
%I A000001
%S A000001 2,79,179,191,211,263,277,313,349,359,409,499,503,509,557,571,599,619,
%T A000001 641,647,673,683,739,769,773,809,857,929,941,947,967,997,1019,1039,1049,
%U A000001 1069,1091,1097,1103,1129,1151,1201,1229,1289,1301,1399,1429,1451,1487
%N A000001 Primes not of form A080435(i)+A080435(j).
%K A000001 nonn
%O A000001 1,1
%A A000001 David Wilson (davidwwilson at attbi.com)
%I A000002
%S A000002 2,8,14,20,50,98,140,200,212,296,338,842,1388,1514,2540,2870,29598
%N A000002 Even elements of A080435.
%K A000002 nonn
%O A000002 1,1
%C A000002 No more values <= 100000.
%A A000002 David Wilson (davidwwilson at attbi.com)

%I A000003
%S A000003 1,2,3,5,8,14,20,23,24,37,43,48,49,55,61,75,90,109,117,118,121,139,141,
%T A000003 157,183,193,199,212,223,229,241,245,271,277,296,301,313,320,321,331,363,
%U A000003 368,393,403,410,422,439,457,468,469,481,491,511,525,530,535,607,665,674
%N A000003 a(1) = 1; a(n) = least k > a(n-1) such that a(i)+k is prime for some a(i) < k, and each
prime of form a(i)+a(j) occurs for unique i <= j.
%K A000003 nonn
%Y A000003 Cf. A000004, A000005, A080435
%O A000003 1,2
%A A000003 David Wilson (davidwwilson at attbi.com)
%I A000004
%S A000004 2,41,59,101,107,233,251,263,281,307,397,409,467,569,619,809,881,1013,
%T A000004 1091,1163,1181,1187,1193,1237,1297,1319,1481,1493,1559,1571,1637,1693,
%U A000004 1697,1801,1871,1901,1907,1931,1979,2087,2099,2111,2153,2179,2207,2267%
%N A000004 Primes not of form A000003(i)+A000003(j).
%K A000004 nonn
%O A000004 1,1
%A A000004 David Wilson (davidwwilson at attbi.com)
%I A000005
%S A000005 2,8,14,20,24,48,90,118,212,296,320,368,410,422,468,530,674,722,812,848,
%T A000005 920,1262,1328,1940,2162,2252,2486,3362,3380,3956,4040,5060,6410,6764,
%U A000005 6920,7256,8840,9284,10580,10802,12308,12770,13190,17960,20792,32720
%N A000005 Even elements of A000003(i)+A000003(j).
%K A000005 nonn
%O A000005 1,1
%A A000005 David Wilson (davidwwilson at attbi.com)

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