A166581 -id:A166581 - cp's OEIS frontend

A166573 Prime numbers containing the string 13.

13, 113, 131, 137, 139, 313, 613, 1013, 1213, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1613, 1913, 2113, 2131, 2137, 2213, 2713, 3137, 3313, 3413, 3613, 4013, 4133, 4139, 4513, 4813, 5113, 5413, 5813, 6113, 6131, 6133, 7013, 7213, 8513

Offset: 1

Vincenzo Librandi, Nov 01 2009

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triskaidekaphobia
Wikipedia, Triskaidekaphobia

Complement of A076805 with respect to A000040.

Cf. A166571, A166572, A166579, A166580, A166581, A166582.

import Data.List (isInfixOf)
a166573 n = a166573_list !! (n-1)
a166573_list = filter (("13" `isInfixOf`) . show) a000040_list
-- Reinhard Zumkeller, Nov 09 2011

p13Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 3}]]; Select[Prime[Range[1000]], p13Q] (* Vincenzo Librandi, Sep 14 2012 *)
Select[Prime[Range[1500]], ! StringFreeQ[ToString[#], "13"] &] (* Vincenzo Librandi, May 03 2015 *)

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,13) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Nov 09 2011

Corrected (313 inserted) by R. J. Mathar, Nov 30 2009

A166582 Primes containing the string 444.

Original entry on oeis.org

4441, 4447, 14447, 14449, 24443, 44417, 44449, 44453, 44483, 44491, 44497, 54443, 54449, 74441, 74449, 84443, 84449, 94441, 94447, 124447, 134443, 144407, 144409, 144413, 144427, 144439, 144451, 144461, 144479, 144481, 144497, 164443, 164447

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A166571-A166573, A166579-A166581.

p444Q[n_] :=  Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 3, 1], {4, 4, 4}]]; Select[Prime[Range[20000]], p444Q] (* Vincenzo Librandi Sep 14 2012 *)
Select[Prime[Range[16000]],SequenceCount[IntegerDigits[#],{4,4,4}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 15 2018 *)

a(n) ~ n log n. - Charles R Greathouse IV, Nov 01 2022

Corrected (144491 replaced by 144497) by R. J. Mathar, Nov 30 2009

A166579 Prime numbers containing the string 17.

Original entry on oeis.org

17, 173, 179, 317, 617, 1117, 1171, 1217, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 2017, 2179, 2417, 2617, 2917, 3217, 3517, 3617, 3917, 4177, 4217, 4517, 4817, 5171, 5179, 5417, 5717, 6173, 6217, 6317, 6917, 7177, 7417

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A166571 - A166573, A166580, A166581, A166582.

isA166579 := proc(n) local dgs,wrks; if isprime(n) then dgs := convert(n,base,10) ; wrks := false; for i from 1 to nops(dgs)-1 do if op(i,dgs) = 7 and op(i+1,dgs) = 1 then return true; end if; od: return false; else false; end if; end proc: for n from 1 to 8000 do if isA166579(n) then printf("%d,",n) ; end if; od: # R. J. Mathar, Nov 30 2009

p17Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 7}]]; Select[Prime[Range[1000]], p17Q] (* Vincenzo Librandi Sep 14 2012 *)
Select[Prime[Range[1000]],SequenceCount[IntegerDigits[#],{1,7}]>0&] (* Harvey P. Dale, Apr 18 2022 *)

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,17) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014

A166571 Prime numbers containing the string 10.

Original entry on oeis.org

101, 103, 107, 109, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 3109, 5101, 5107, 6101, 7103, 7109, 8101, 9103, 9109, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A166572, A166573, A166579, A166580, A166581, A166582.

p10Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 0}]]; Select[Prime[Range[1250]], p10Q] (* Vincenzo Librandi, Sep 14 2012 *)

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,10) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014

Corrected (1087 inserted) by R. J. Mathar, Nov 30 2009

A166580 Prime numbers containing the string 222.

Original entry on oeis.org

2221, 12227, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 42221, 42223, 42227, 52223, 72221, 72223, 72227, 72229, 82223, 92221, 92227, 102229, 112223, 122201, 122203, 122207, 122209, 122219, 122231, 122251, 122263, 122267, 122273, 122279, 122299, 132229, 142223

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A243527, A166581, A166582, A167281, A131645, A167282, A167290, A167292.

res := []; for n in [1..15000] do p := NthPrime(n); digits := IntegerToSequence(p); for i in [1..#digits - 2] do if digits[i..i+2] eq [2,2,2] then Append(~res, p); break; end if; end for; end for; res; // Vincenzo Librandi, Jul 16 2025

p222Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 3, 1], {2, 2, 2}]]; Select[Prime[Range[15000]], p222Q] (* Vincenzo Librandi Sep 14 2012 *)
Select[Prime[Range[12000]],SequenceCount[IntegerDigits[#],{2,2,2}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 08 2017 *)

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,222) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014

A257667 Primes containing a digit 5.

Original entry on oeis.org

5, 53, 59, 151, 157, 251, 257, 353, 359, 457, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 653, 659, 751, 757, 853, 857, 859, 953, 1051, 1151, 1153, 1259, 1451, 1453, 1459, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579

Offset: 1

Vincenzo Librandi, May 03 2015

Subsequence of primes of A011535. - Michel Marcus, May 03 2015

Primes in A062671. - Bruno Berselli, May 03 2015

Shujing Lyu, Table of n, a(n) for n = 1..100000

Cf. prime numbers containing the string k: A208270 (k=1), A208272 (k=2), A212525 (k=3), this sequence (k=5), A257668 (k=7), A166571 (k=10), A166572 (k=11), A243529 (k=12), A166573 (k=13), A243530 (k=14), A243531 (k=15), A243532 (k=16), A166579 (k=17), A243527 (k=111), A166580 (k=222), A166581 (k=333), A166582 (k=444).

Cf. A011535, A062671, A243531 (subsequence).

[p: p in PrimesUpTo(1600) | 5 in Intseq(p)];

Select[Prime[Range[250]], ! StringFreeQ[ToString[#], "5"] &]

forprime(p=1, 1600, if(vecsearch(vecsort(digits(p)), 5), print1(p, ", "))) \\ Derek Orr, May 05 2015; corrected by Michel Marcus, Oct 30 2023

[p for p in primes(1600) if 5 in p.digits(base=10)] # Bruno Berselli, May 03 2015

a(n) ~ n log n. - Charles R Greathouse IV, Nov 01 2022

A166572 Prime numbers containing the string 11.

Original entry on oeis.org

11, 113, 211, 311, 811, 911, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1511, 1811, 2011, 2111, 2113, 2311, 2411, 2711, 3011, 3119, 3511, 3911, 4111, 4211, 5011, 5113, 5119, 5711, 6011, 6113, 6211, 6311, 6911, 7211, 7411

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A166571, A166573, A166579, A166580, A166581, A166582.

isA166572 := proc(n) local dgs,wrks; if isprime(n) then dgs := convert(n,base,10) ; wrks := false; for i from 1 to nops(dgs)-1 do if op(i,dgs) = 1 and op(i+1,dgs) = 1 then return true; end if; od: return false; else false; end if; end proc: for n from 1 to 8000 do if isA166572(n) then printf("%d,",n) ; end if; od: # R. J. Mathar, Nov 30 2009

p11Q[n_]: = Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 1}]] Select[Prime[Range[1000]], p11Q] (* Vincenzo Librandi, Sep 14 2012 *)
Select[Prime[Range[1000]],SequenceCount[IntegerDigits[#],{1,1}]>0&] (* Harvey P. Dale, Sep 24 2022 *)

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,11) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014

A167292 Primes containing 999 as a substring.

Original entry on oeis.org

1999, 2999, 4999, 8999, 13999, 19991, 19993, 19997, 25999, 32999, 35999, 41999, 49991, 49993, 49999, 52999, 56999, 59999, 69991, 69997, 70999, 71999, 73999, 77999, 79997, 79999, 85999, 94999, 98999, 99901, 99907, 99923, 99929, 99961

Offset: 1

Vincenzo Librandi, Nov 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Superset of A230202.
Cf. A166571, A166572, A166573, A166579.
Cf. A243527, A166580, A166581, A166582, A167281, A167282, A167290.

p999Q[n_] := Module[{idn=IntegerDigits[n]}, MemberQ[Partition[idn, 3, 1], {9, 9, 9}]]; Select[Prime[Range[10000]], p999Q] (* Vincenzo Librandi, Sep 15 2013 *)

A243527 Prime numbers containing the string 111.

Original entry on oeis.org

1117, 2111, 4111, 8111, 10111, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 16111, 22111, 25111, 26111, 28111, 35111, 40111, 41113, 41117, 44111, 47111, 50111, 58111, 65111, 68111, 70111, 71119, 79111, 80111

Offset: 1

Vincenzo Librandi, Jun 06 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. prime numbers containing the string kkk: this sequence (k=1), A166580 (k=2), A166581 (k=3), A166582 (k=4), A167281 (k=5), A131645 (k=6), A167282 (k=7), A167290 (k=8), A167292 (k=9).

Select[Prime[Range[90000]], !StringFreeQ[ToString[#], "111"]&]

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,111) \\ Charles R Greathouse IV, Jun 20 2014

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014

A386247 Primes containing 000 as a substring.

Original entry on oeis.org

10007, 10009, 40009, 70001, 70003, 70009, 90001, 90007, 100003, 100019, 100043, 100049, 100057, 100069, 130003, 140009, 150001, 160001, 160009, 170003, 180001, 180007, 200003, 200009, 200017, 200023, 200029, 200033, 200041, 200063, 200087, 220009, 230003, 240007

Offset: 1

Alois P. Heinz, Jul 16 2025

Differs from A164968 first at n=10: a(10) = 100019 < 200003 = A164968(10).

Alois P. Heinz, Table of n, a(n) for n = 1..20761

Cf. A000040, A164968, A243527, A166580, A166581, A166582, A167281, A131645, A167282, A167290, A167292, A386240.

Select[Prime[Range[1230, 25000]], StringContainsQ[IntegerString[#], "000"] &] (* Paolo Xausa, Jul 19 2025 *)

cp's OEIS Frontend

A166573 Prime numbers containing the string 13.

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A166582 Primes containing the string 444.

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A166579 Prime numbers containing the string 17.

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A166571 Prime numbers containing the string 10.

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A166580 Prime numbers containing the string 222.

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A257667 Primes containing a digit 5.

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A166572 Prime numbers containing the string 11.

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