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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

Table of n, a(n) for n=1..39.

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 November 18 02:03 EST 2019. Contains 329242 sequences. (Running on oeis4.)