A114754
Smallest prime of the form: n successive positive integers in ascending order followed by a 1.
Original entry on oeis.org
11, 10111, 1231, 67891, 9101112131, 3456781, 91011121314151, 45678910111, 1234567891, 303132333435363738391, 12345678910111, 939495969798991001011021031041, 91011121314151617181920211
Offset: 1
a(2) = 10111= 10 followed by 11 followed by 1.
a(3) = 1231, three successive positive integers 1,2,3 in ascending order followed by a 1.
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a[n_]:=(For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m, m+n-1}]);!PrimeQ[10FromDigits[v]+1], m++ ];10FromDigits[v]+1);Table[a[n], {n, 14}] - Farideh Firoozbakht
f[n_] := Block[{t = Range@n}, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {1}]; !PrimeQ@p, t++ ]; p]; Array[f, 13] (* Robert G. Wilson v *)
A114758
Smallest prime of the form: n successive positive integers in descending order followed by a 1.
Original entry on oeis.org
11, 211, 5431, 76541, 17161514131, 1211109871, 98765431, 876543211, 9876543211, 242322212019181716151, 11109876543211, 1131121111101091081071061051041031021, 555453525150494847464544431
Offset: 1
a(4) = 76541, four successive positive integers 7,6,5,4 in descending order followed by a 1.
-
f:= proc(n) local k,p,j;
for k from 0 do
p:= parse(cat(seq(k+j,j=n .. 1,-1), 1));
if isprime(p) then return p fi
od
end proc:map(f, [$1..15]); # Robert Israel, Apr 03 2023
-
a[n_]:=(For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m+n-1, m, -1}]);!PrimeQ[10FromDigits[v]+1], m++ ];10FromDigits[v]+1);Table[a[n], {n, 14}] (* Farideh Firoozbakht, Jan 02 2006 *)
f[n_] := Block[{t = Reverse@Range@n}, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {1}]; ! PrimeQ@p, t++ ]; p]; Array[f, 13] (* Robert G. Wilson v, Jan 03 2006 *)
A114756
Smallest prime of the form: n successive positive integers in ascending order followed by a 7.
Original entry on oeis.org
17, 127, 1237, 12347, 123457, 56789107, 456789107, 3456789107, 4567891011127, 616263646566676869707, 13141516171819202122237, 2021222324252627282930317, 151617181920212223242526277
Offset: 1
a(4) = 12347, four successive positive integers 1,2,3,4 in ascending order followed by a 7.
-
a[n_]:=(For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m, m+n-1}]);!PrimeQ[10FromDigits[v]+7], m++ ];10FromDigits[v]+7);Table[a[n], {n, 14}] - Farideh Firoozbakht
f[n_] := Block[{t = Range@n}, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {7}]; !PrimeQ@p, t++ ]; p]; Array[f, 14] (* Robert G. Wilson v *)
Table[SelectFirst[10 FromDigits[Flatten[IntegerDigits/@#]]+7&/@ Partition[ Range[1000],n,1],PrimeQ],{n,20}] (* Harvey P. Dale, Jan 29 2022 *)
A108145
Smallest prime consisting of n successive positive integers in descending order followed by a 9. a(3*k) = 0 as no such prime exists.
Original entry on oeis.org
19, 439, 0, 262524239, 765439, 0, 109876549, 1098765439, 0, 504948474645444342419, 27262524232221201918179, 0, 2019181716151413121110989, 64636261605958575655545352519, 0
Offset: 1
a(2) = 439, two successive positive integers 4,3 in descending order followed by a 9.
a(4) = 262524239 four successive positive integers 26,25,24,23 in descending order followed by a 9.
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a[n_]:=If[Mod[n, 3]==0, 0, (For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m+n-1, m, -1}]);!PrimeQ[10FromDigits[v]+9], m++ ];10FromDigits[v]+9)];Table[a[n], {n, 16}] (* Farideh Firoozbakht *)
f[n_] := Block[{t = Reverse@Range@n}, If[ Mod[n, 3] == 0, 0, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {9}]; !PrimeQ@p, t++ ]; p]]; Array[f, 16] (* Robert G. Wilson v *)
A114755
Smallest prime of the form: n successive positive integers in ascending order followed by a 3. a(3k) = 0 as no such prime exists.
Original entry on oeis.org
13, 233, 0, 12343, 345673, 0, 5678910113, 54555657585960613, 0, 373839404142434445463, 17181920212223242526273, 0, 2345678910111213143, 23242526272829303132333435363, 0, 8910111213141516171819202122233
Offset: 1
a(4) = 12343, four successive positive integers 1,2,3,4 in ascending order followed by a 3.
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a[n_]:=If[Mod[n, 3]==0, 0, (For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m, m+n-1}]);!PrimeQ[10FromDigits[v]+3], m++ ];10FromDigits[v]+3)];Table[a[n], {n, 17}] - Farideh Firoozbakht
f[n_] := Block[{t = Range@n}, If[ Mod[n, 3] == 0, 0, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {3}]; !PrimeQ@p, t++ ]; p]]; Array[f, 20] (* Robert G. Wilson v *)
A114757
Smallest prime of the form: n successive positive integers in ascending order followed by a 9. a(3k) = 0 as no such prime exists.
Original entry on oeis.org
19, 239, 0, 23459, 345679, 0, 23456789, 234567899, 0, 2345678910119, 6789101112131415169, 0, 313233343536373839404142439, 36373839404142434445464748499, 0, 123456789101112131415169
Offset: 1
a(4) = 23459, four successive positive integers 2,3,4,5 in ascending order followed by a 9.
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a[n_]:=If[Mod[n, 3]==0, 0, (For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m, m+n-1}]);!PrimeQ[10FromDigits[v]+9], m++ ];10FromDigits[v]+9)];Table[a[n], {n, 17}] - Farideh Firoozbakht
f[n_] := Block[{t = Range@n}, If[ Mod[n, 3] == 0, 0, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {9}]; !PrimeQ@p, t++ ]; p]]; Array[f, 16] (* Robert G. Wilson v *)
A114759
Smallest prime of the form: n successive positive integers in descending order followed by a 3. a(3k) = 0 as no such prime exists.
Original entry on oeis.org
13, 433, 0, 54323, 654323, 0, 292827262524233, 987654323, 0, 1716151413121110983, 181716151413121110983, 0, 1413121110987654323, 27262524232221201918171615143, 0, 1716151413121110987654323
Offset: 1
a(4) = 54323, four successive positive integers 5,4,3,2 in descending order followed by a 3.
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a[n_]:=If[Mod[n, 3]==0, 0, (For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m+n-1, m, -1}]);!PrimeQ[10FromDigits[v]+3], m++ ];10FromDigits[v] +3)];Table[a[n], {n, 17}] - Farideh Firoozbakht
f[n_] := Block[{t = Reverse@Range@n}, If[Mod[n, 3] == 0, 0, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {3}]; ! PrimeQ@p, t++ ]; p]]; Array[f, 18] (* Robert G. Wilson v *)
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