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A080155
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a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.
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1
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2, 3, 11, 31, 47, 229, 251, 577, 857, 859, 911, 1123, 1223, 1297, 1571, 2161, 2417, 2551, 2879, 3319, 5273, 6121, 6947, 7603, 8273, 12721, 12953, 13291, 15683, 16453, 17207, 18133, 20399, 23743, 23909, 25849, 28277, 28879, 35291, 35461, 36107
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| See A073640 for the sequence involving concatenation of 2 successive terms, A080153 for 3 successive terms. Primeness is established using Maple's isprime() function, so later terms should be regarded as "probable".
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FORMULA
| For any n>1, a(n) is prime and a(n) > a(n-1). a(n) is the smallest prime for which a(1)//a(2)//...//a(n) is prime. // denotes concatenation.
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EXAMPLE
| E.g. a(5)=47 since this is the smallest prime>a(4) which, when concatenated with the concatenation of a(1) to a(4) (=231131), also yields a prime, in this case 23113147.
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MAPLE
| with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i], i=1..nops(pout)), p)): if (isprime(d)) then pout := [op(pout), p]: nout := [op(nout), n]: fi: od: pout;
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MATHEMATICA
| f[s_List]:=Block[{p=NextPrime@s[[-1]], pp=FromDigits@Flatten[IntegerDigits/@s]}, While[!PrimeQ[pp*10^Floor[Log[10, p]+1]+p], p=NextPrime@p]; Append[s, p]]; Nest[f, {2}, 40]
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CROSSREFS
| Cf. A073640, A080152, A080153, A080154.
Cf. A033679, A069603, A074338. [Zak Seidov (zakseidov(AT)yahoo.com), Oct 09 2009]
Sequence in context: A038987 A142957 A191058 * A032357 A144056 A062630
Adjacent sequences: A080152 A080153 A080154 * A080156 A080157 A080158
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KEYWORD
| nonn,base
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AUTHOR
| Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003
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