A068166
Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 1.
Original entry on oeis.org
1, 11, 101, 1013, 10103, 100103, 1001003, 10010023, 100010023, 1000100239, 10001000239, 100010002039, 1000100020319, 10001000200319, 100001000200319, 1000010002000319, 10000100002000319, 100001000020003109, 1000010000200031039, 10000100002000310329
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 11 are 101, 113, 131, 181, 191, 211, 311, etc. and the smallest is 101, hence a(3) = 101.
A068169
Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 4.
Original entry on oeis.org
4, 41, 241, 2141, 21341, 213461, 2123461, 21123461, 211234561, 2112343561, 21123043561, 211230043561, 2112030043561, 21112030043561, 211120030043561, 2110120030043561, 21101020030043561, 211010200230043561, 2110102002300430561, 21010102002300430561
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 41 are 241, 419, 421 etc... a(3)= 241 is the smallest.
A068170
Define an increasing sequence as follows. Given the first term, called the seed (the seed need not have the property of the remaining terms of the sequence), subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 5.
Original entry on oeis.org
5, 53, 353, 3253, 30253, 130253, 1300253, 10300253, 100300253, 1003002053, 10030020503, 100300200503, 1003002050503, 10013002050503, 100130002050503, 1001300002050503, 10013000020503503, 100013000020503503, 1000130000205035083, 10001300002015035083
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 53 are 353, 523, ...; a(3) = 353 is the smallest.
A030456
a(0) = 2; a(n) is smallest prime containing a(n-1) as substring.
Original entry on oeis.org
2, 23, 223, 1223, 12239, 122393, 1223939, 12239393, 122393939, 1223939399, 12239393993, 122393939933, 12239393993311, 412239393993311, 8412239393993311, 78412239393993311, 2378412239393993311, 23784122393939933111, 2623784122393939933111, 26237841223939399331111
Offset: 0
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FromDigits /@ Nest[Append[#, Block[{p = NextPrime@ FromDigits@ #[[-1]], d}, While[Length@ SequencePosition[Set[d, IntegerDigits@ p], #[[-1]]] == 0, p = NextPrime@ p]; d]] &, {{2}}, 7] (* Michael De Vlieger, Feb 26 2018 *)
A068171
Define an increasing sequence as follows: Given the first term called the seed (the seed need not have the property of the sequence.), subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 6.
Original entry on oeis.org
6, 61, 461, 3461, 33461, 332461, 3132461, 31320461, 313204061, 3130204061, 23130204061, 231302004061, 2131302004061, 21313020024061, 213130200240161, 2131230200240161, 12131230200240161, 121312302002401613, 1210312302002401613, 12103123020020401613, 121031230200203401613, 1210312300200203401613
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 61 are 461, 619, 641, etc...a(3) = 461 is the smallest.
A068172
Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 7.
Original entry on oeis.org
7, 17, 107, 1087, 10487, 104087, 1024087, 10024087, 100024087, 1000124087, 10001240087, 100012400837, 1000124008327, 10000124008327, 100001124008327, 1000011224008327, 10000110224008327, 100001100224008327, 1000010100224008327, 10000101002240083271, 100001010022400283271, 1000010100221400283271
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 17 are 107,127, 137, etc...a(3) = 107 is the smallest.
A068173
Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 8.
Original entry on oeis.org
8, 83, 283, 1283, 12583, 112583, 1102583, 11002583, 110025803, 1010025803, 10100258303, 101002258303, 1010022508303, 10100225080303, 101002250803093, 1010022508030793, 10100225080303793, 101002250803030793, 1010022508030305793, 10100224508030305793
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 89 are 389, 809, etc...a(3) = 389 is the smallest.
A242904
a(n+1) is the smallest prime > a(n) such that the digits of a(n) are all (with multiplicity) contained in the digits of a(n+1), with a(1)=2.
Original entry on oeis.org
2, 23, 223, 1223, 2213, 3221, 10223, 12203, 20123, 20231, 21023, 22013, 22031, 23021, 23201, 102023, 102203, 200231, 201203, 202031, 220013, 220301, 300221, 322001, 1002263, 1002623, 1060223, 1062203, 1202063, 1202603, 1600223, 2002361, 2002613, 2003621
Offset: 1
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with(numtheory):lst:={2}:nn:=150000:x0:=convert(2,base,10):n0:=nops(x0):
for n from 2 to nn do:
p:=ithprime(n):x:=convert(p,base,10):
x1:=x:n1:=nops(x):c:=0:
for i from 1 to n0 do:
ii:=0:
for j from 1 to n1 while(ii=0)do:
if x0[i]=x[j]
then
c:=c+1:x[j]:=99:ii:=1:
else
fi:
od:
od:
if c=n0
then
lst:=lst union {p}:n0:=n1:x0:=x1:
else
fi:
od:
print(lst):
A068174
Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. This is the prime sequence with the seed a(1) = 9.
Original entry on oeis.org
9, 19, 109, 1009, 10009, 100019, 1000159, 10001569, 100001569, 1000015069, 10000135069, 100001350649, 1000013500649, 10000130500649, 100001303500649, 1000013032500649, 10000103032500649, 100001030325003649, 1000010130325003649, 10000101303250036493
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 19 are 109, 139, 149, 179, 199 etc. and a(3) = 109 is the smallest.
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f[n_] := Block[{b = PadLeft[ IntegerDigits[n], Floor[ Log[10, n] + 1]], k = 0}, While[ !PrimeQ[ FromDigits[ Insert[b, k, -2]]], k++ ]; FromDigits[ Insert[b, k, -2]]]; NestList[ f, 9, 18]
A068168
Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 3.
Original entry on oeis.org
3, 13, 103, 1013, 10103, 100103, 1001003, 10010023, 100010023, 1000100239, 10001000239, 100010002039, 1000100020319, 10001000200319, 100001000200319, 1000010002000319, 10000100002000319, 100001000020003109, 1000010000200031039, 10000100002000310329
Offset: 1
The primes obtained by inserting/placing a digit in a(2) = 13 are 113,131,313 etc... a(3)= 113 is the smallest.
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a:= proc(n) option remember; local s, w, m;
if n=1 then 3
else w:=a(n-1); s:=""||w; m:=length(s);
min(select(x->length(x)=m+1 and isprime(x),
{seq(seq(parse(cat(seq(s[h], h=1..i), j,
seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])
fi
end:
seq(a(n), n=1..23); # Alois P. Heinz, Nov 07 2014
Showing 1-10 of 11 results.
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