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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
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
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
KEYWORD
base,fini,nonn,uned
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 13 2010
STATUS
approved