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 A176254 Smallest primes in growing order where the parts of compositions of integer 8 = 2^3 used as decimal digits enable primes. 0
 17, 53, 71, 233, 251, 431, 521, 1061, 1151, 1223, 1511, 2141, 2213, 2411, 3023, 3041, 3221, 4013, 4211, 6011, 10133, 10313, 10331, 11213, 11321, 11411, 12041, 12113, 13121, 20123, 20231, 21221, 23021, 30113, 31121, 41201, 50111, 100043, 101141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See comments and references of A176251. 22 partitions of 8 (5 with only even naturals enable no primes): 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, 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. 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. List of classes, primes in each class in growing order: (1) 17, 71 (2) 1061, 6011 (3) 53 (4) 251, 521 (5) 1151, 1511, 50111 (6) 431, 3041, 4013, 100043 (7) 2141, 2411, 4211, 12041, 41201, 104021 (8) 11411, 101141, 140111, 411011 (9) 233, 3023 (10) 10133, 10313, 10331, 30113, 303011, 3000131 (11) 1223, 2213, 3221, 20123, 20231, 23021 (12) 11213, 11321, 12113, 13121, 31121, 112031, 130211, 210113, 210131, 301211, 302111, 1001123, 1021301, 1023101, 2010311, 2301011 (13) 113111, 131111, 311111, 1110311, 1111013, 1111031 (14) 21221, 122021, 202121, 222011 (15) 112121, 1011221, 1120211, 1210211, 2011211, 2121011, 10210121, 12210101, 21001121, 200210111 (16) 1111211, 10111121, 11201111, 101121011, 102110111, 210110111 (17) 101111111 List of 40th up to 81st term: 104021, 112031, 112121, 113111, 122021, 130211, 131111, 140111, 202121, 210113, 210131, 222011, 301211, 302111, 303011, 311111, 411011, 1001123, 1011221, 1021301, 1023101, 1110311, 1111013, 1111031, 1111211, 1120211, 1210211, 2010311, 2011211, 2121011, 2301011, 3000131, 10111121, 10210121, 11201111, 12210101, 21001121, 101111111, 101121011, 102110111, 200210111, 210110111 LINKS EXAMPLE 17 = prime(7), 1st term 53 = prime(16), 2nd term 71 = prime(20), 3rd term 11411 = prime(1377) = palprime(5^2), 26th term 1120211 = prime(87179) = palprime(130), 65th term 210110111 = prime(11607340), 81st term CROSSREFS Cf. A000041, A046704, A075177, A091939, A176009, A176251, A176252. Sequence in context: A295869 A061242 A062343 * A287311 A285225 A044119 Adjacent sequences:  A176251 A176252 A176253 * A176255 A176256 A176257 KEYWORD base,fini,nonn,uned AUTHOR Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 13 2010 STATUS approved

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Last modified August 19 20:38 EDT 2022. Contains 356231 sequences. (Running on oeis4.)