A166572 -id:A166572 - 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

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

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

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 *)

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A166573 Prime numbers containing the string 13.

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A166571 Prime numbers containing the string 10.

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A257667 Primes containing a digit 5.

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A167292 Primes containing 999 as a substring.

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