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%I #5 Apr 16 2014 00:39:43
%S 17,53,71,233,251,431,521,1061,1151,1223,1511,2141,2213,2411,3023,
%T 3041,3221,4013,4211,6011,10133,10313,10331,11213,11321,11411,12041,
%U 12113,13121,20123,20231,21221,23021,30113,31121,41201,50111,100043,101141
%N Smallest primes in growing order where the parts of compositions of integer 8 = 2^3 used as decimal digits enable primes.
%C See comments and references of A176251.
%C 22 partitions of 8 (5 with only even naturals enable no primes):
%C 8, 7+1, 6+2, 6+1+1, 5+3, 5+2+1, 5+1+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1, 4+1+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1,
%C 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, 1+1+1+1+1+1+1+1.
%C Compositions of 8 (order of "parts" matters) in 17 = prime(7) "classes", which with included zeros enable primes, so this sequence has 81 = 3^4 terms.
%C List of classes, primes in each class in growing order:
%C (1) 17, 71 (2) 1061, 6011 (3) 53 (4) 251, 521 (5) 1151, 1511, 50111
%C (6) 431, 3041, 4013, 100043 (7) 2141, 2411, 4211, 12041, 41201, 104021
%C (8) 11411, 101141, 140111, 411011 (9) 233, 3023
%C (10) 10133, 10313, 10331, 30113, 303011, 3000131
%C (11) 1223, 2213, 3221, 20123, 20231, 23021
%C (12) 11213, 11321, 12113, 13121, 31121, 112031, 130211, 210113, 210131, 301211, 302111, 1001123, 1021301, 1023101, 2010311, 2301011
%C (13) 113111, 131111, 311111, 1110311, 1111013, 1111031
%C (14) 21221, 122021, 202121, 222011
%C (15) 112121, 1011221, 1120211, 1210211, 2011211, 2121011, 10210121, 12210101, 21001121, 200210111
%C (16) 1111211, 10111121, 11201111, 101121011, 102110111, 210110111 (17) 101111111
%C List of 40th up to 81st term:
%C 104021, 112031, 112121, 113111, 122021, 130211, 131111, 140111, 202121, 210113,
%C 210131, 222011, 301211, 302111, 303011, 311111, 411011, 1001123, 1011221, 1021301,
%C 1023101, 1110311, 1111013, 1111031, 1111211, 1120211, 1210211, 2010311, 2011211, 2121011,
%C 2301011, 3000131, 10111121, 10210121, 11201111, 12210101, 21001121, 101111111, 101121011, 102110111,
%C 200210111, 210110111
%e 17 = prime(7), 1st term
%e 53 = prime(16), 2nd term
%e 71 = prime(20), 3rd term
%e 11411 = prime(1377) = palprime(5^2), 26th term
%e 1120211 = prime(87179) = palprime(130), 65th term
%e 210110111 = prime(11607340), 81st term
%Y Cf. A000041, A046704, A075177, A091939, A176009, A176251, A176252.
%K base,fini,nonn,uned
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 13 2010
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