A167282 -id:A167282 - cp's OEIS frontend

A166580 Prime numbers containing the string 222.

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

A167290 Primes containing 888 as a substring.

Original entry on oeis.org

8887, 48883, 48889, 58889, 68881, 78887, 78889, 88801, 88807, 88811, 88813, 88817, 88819, 88843, 88853, 88861, 88867, 88873, 88883, 88897, 98887, 108881, 108883, 108887, 138883, 138889, 158881, 168887, 178889, 188801, 188827, 188831, 188833

Offset: 1

Vincenzo Librandi, Nov 01 2009

nonn

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

Cf. A166571 - A166573, A166579 - A166582, A167281, A167282.

p888Q[n_] := Module[{idn=IntegerDigits[n]}, MemberQ[Partition[idn, 3, 1], {8, 8, 8}]]; Select[Prime[Range[20000]], p888Q] (* Vincenzo Librandi, Sep 15 2013 *)

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

A386240 Primes containing the digit string "007" in their decimal representation.

Original entry on oeis.org

4007, 6007, 9007, 10007, 10079, 12007, 13007, 16007, 20071, 24007, 30071, 36007, 45007, 50077, 60077, 61007, 64007, 70079, 78007, 80071, 80077, 82007, 88007, 90007, 90071, 90073, 94007, 97007, 100703, 100733, 100741, 100747, 100769, 100787, 100799, 103007, 108007

Offset: 1

Hugo Pfoertner, Jul 16 2025

Could also be called "James Bond" primes.

Alois P. Heinz, Table of n, a(n) for n = 1..36628
Karl-Heinz Hofmann, Ascii search picture. Who can find the first 5 terms?
Q-branch staff, The origin of James Bond: unveiling the history behind 007, 21 February 2024.
Reddit, We never saw Daniel Craig's Bond in his prime
Joe Roberts, How James Bond Became 007 (& How Its Meaning Has Changed), Jul 7, 2020.
Joe Roberts, How Did James Bond Get The Codename 007? A Canceled Movie Almost Gave Us The Answer, Feb 24, 2025.

Cf. A386247, A166580, A167282, A193552.

q:= n-> isprime(n) and searchtext("007", ""||n)>0:
select(q, [$1..110000])[];  # Alois P. Heinz, Jul 17 2025

Select[Prime[Range[553, 12000]], StringContainsQ[IntegerString[#], "007"] &] (* Paolo Xausa, Jul 17 2025 *)

is(n) = if(!isprime(n), return(0)); while(n > 10, if(n%1000==7, return(1)); n\=10); 0 \\ David A. Corneth, Jul 17 2025

from sympy import sieve
print([sieve[n] for n in range(1,10200) if "007" in str(sieve[n])]) # Karl-Heinz Hofmann, Jul 17 2025

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 *)

A298729 Prime numbers whose decimal expansion includes a substring of seven consecutive 7's.

Original entry on oeis.org

137777777, 177777773, 177777779, 197777777, 307777777, 347777777, 437777777, 527777777, 547777777, 577777777, 587777777, 647777777, 697777777, 777777701, 777777739, 777777743, 777777751, 777777799, 787777777, 827777777, 947777777, 967777777, 1247777777, 1277777771, 1277777773, 1457777777, 1487777777

Offset: 1

Yohei Furutono, Jan 25 2018

Cf. A102764, A167282, A108844, A083978.

s = {7, 7, 7, 7, 7, 7, 7}; lst = {}; k = 1; While[k < 10001, l = 1; il = 12;
While[l < il, p = FromDigits@ Flatten@ Insert[ IntegerDigits[k, 10, 10], s, l];
  If[PrimeQ@ p, AppendTo[lst, p]]; l++]; k++]; Union@ lst (* Robert G. Wilson v, Feb 08 2018 *)

is(n) = my(v=vector(7, x, 7), d=digits(n)); for(k=1, #d-6, if([d[k], d[k+1], d[k+2], d[k+3], d[k+4], d[k+5], d[k+6]]==v, return(1))); 0
forprime(p=1, , if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Mar 06 2018

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A166580 Prime numbers containing the string 222.

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Magma

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A167290 Primes containing 888 as a substring.

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A167292 Primes containing 999 as a substring.

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A243527 Prime numbers containing the string 111.

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A386240 Primes containing the digit string "007" in their decimal representation.

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Maple

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A386247 Primes containing 000 as a substring.

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Mathematica

A298729 Prime numbers whose decimal expansion includes a substring of seven consecutive 7's.

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Mathematica

PARI