A034844 -id:A034844 - cp's OEIS frontend

A083185 Palindromic primes using only nonprime digits (0,1,4,6,8,9).

11, 101, 181, 191, 919, 10601, 11411, 16061, 16661, 18181, 18481, 19891, 19991, 91019, 94049, 94649, 94849, 94949, 96469, 98689, 1008001, 1114111, 1160611, 1180811, 1186811, 1190911, 1196911, 1409041, 1411141, 1444441, 1461641

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 26 2003

Harvey P. Dale, Table of n, a(n) for n = 1..100
P. De Geest, World!Of Palindromic Primes

Cf. A045336, A019546, A002385.

Palindromes in A034844.

Select[ Prime[ Range[111500]], IntegerDigits[ # ] == Reverse[ IntegerDigits[ # ]] && Union[ Join[ IntegerDigits[ # ], {0, 1, 4, 6, 8, 9}]] == {0, 1, 4, 6, 8, 9} & ]
Select[Prime[Range[120000]],PalindromeQ[#]&&NoneTrue[IntegerDigits[#], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 08 2018 *)

Edited and extended by Patrick De Geest, Jun 11 2003

A092624 Numbers with exactly two prime digits.

Original entry on oeis.org

22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 122, 123, 125, 127, 132, 133, 135, 137, 152, 153, 155, 157, 172, 173, 175, 177, 202, 203, 205, 207, 212, 213, 215, 217, 220, 221, 224, 226, 228, 229, 230, 231, 234, 236, 238, 239, 242, 243, 245

Offset: 1

Jani Melik, Apr 11 2004

A193238(a(n))=2; subsequence of A118950. [Reinhard Zumkeller, Jul 19 2011]

			25 has two prime digits, 2 and 5;
207 has two prime digits, 2 and 7.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A034895, A046034, A085557, A019546, A034844.

Cf. A084984, A092620, A092625.

import Data.List (elemIndices)
a092624 n = a092624_list !! (n-1)
a092624_list = elemIndices 2 a193238_list
-- Reinhard Zumkeller, Jul 19 2011

stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr_nd:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( ts_stpf(i) = 2) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_nd(500);

Select[Range[300],Count[IntegerDigits[#],?PrimeQ]==2&] (* _Harvey P. Dale, Apr 20 2025 *)

A092625 Numbers with exactly three prime digits.

Original entry on oeis.org

222, 223, 225, 227, 232, 233, 235, 237, 252, 253, 255, 257, 272, 273, 275, 277, 322, 323, 325, 327, 332, 333, 335, 337, 352, 353, 355, 357, 372, 373, 375, 377, 522, 523, 525, 527, 532, 533, 535, 537, 552, 553, 555, 557, 572, 573, 575, 577, 722, 723, 725

Offset: 1

Jani Melik, Apr 11 2004

It is the same as A046034 from two digit numbers from 22 up to four digit numbers from 1222.

A193238(a(n))=3; subsequence of A118950. [Reinhard Zumkeller, Jul 19 2011]

			222 has three prime digits, three times 2;
1235 has three prime digits, 2, 3 and 5.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A034895, A046034, A085557, A019546, A034844.

Cf. A084984, A092620, A092624.

import Data.List (elemIndices)
a092625 n = a092625_list !! (n-1)
a092625_list = elemIndices 3 a193238_list
-- Reinhard Zumkeller, Jul 19 2011

stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr_nt:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( ts_stpf(i) = 3) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_nt(2000);

Select[Range[800],Total[Boole[PrimeQ[IntegerDigits[#]]]]==3&] (* Harvey P. Dale, Dec 31 2023 *)

A152312 Primes without odd prime digits.

Original entry on oeis.org

2, 11, 19, 29, 41, 61, 89, 101, 109, 149, 181, 191, 199, 211, 229, 241, 269, 281, 401, 409, 419, 421, 449, 461, 491, 499, 601, 619, 641, 661, 691, 809, 811, 821, 829, 881, 911, 919, 929, 941, 991, 1009, 1019, 1021, 1049, 1061

Offset: 1

Omar E. Pol, Dec 02 2008

Cf. A019546, A034844, A087363.

A179335 a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 3, 7, 19, 2, 2, 3, 3, 41, 3, 7, 3, 5, 61, 7, 7, 3, 7, 3, 89, 7, 101, 3, 7, 109, 3, 2, 3, 3, 3, 149, 5, 5, 3, 7, 3, 7, 181, 19, 3, 7, 19, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 401, 409, 19, 2, 3, 3, 3, 3, 449, 5, 61, 3, 7, 7, 7

Offset: 1

Reinhard Zumkeller, Jul 11 2010

a(n) < 10 iff prime(n) is in A179336;

a(n) = prime(n) iff prime(n) is in A033274. [Corrected by M. F. Hasler, Aug 27 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A070024, A019546, A092629, A104250, A019546, A034844, A179336, A193238.

A179335(n)={my(p=prime(n),m=0,M); for(d=1,n, M=10^d; n=p; until(n<=M || !n\=10, isprime(n%M) & (!m || m>n%M) & m=n%M); m & return(m))} \\ M. F. Hasler, Aug 27 2012

from sympy import isprime, prime
def a(n):
    s = str(prime(n))
    ss = set(int(s[i:i+1+l]) for i in range(len(s)) for l in range(len(s)))
    return min(t for t in ss if isprime(t))
print([a(n) for n in range(1, 94)]) # Michael S. Branicky, Jun 29 2022

A155024 Primes with distinct nonprime digits.

Original entry on oeis.org

19, 41, 61, 89, 109, 149, 401, 409, 419, 461, 491, 601, 619, 641, 691, 809, 941, 1049, 1069, 1409, 1489, 1609, 4019, 4091, 4691, 4801, 4861, 6089, 6091, 6481, 6491, 6841, 8069, 8419, 8461, 8609, 8641, 8941, 9041, 9461, 9601, 14869, 18049, 40169, 40189

Offset: 1

Juri-Stepan Gerasimov, Jan 19 2009

Nonprime digits = 0, 1, 4, 6, 8 and 9.

There are only 153 terms in this sequence, all of which are in the linked b-file. - Harvey P. Dale, Dec 30 2012

Harvey P. Dale, Table of n, a(n) for n = 1..153

Cf. A000040, A141468.

Cf. A029743, A034844. - R. J. Mathar, Mar 29 2010

Select[Prime[Range[5000]],Union[PrimeQ[IntegerDigits[#]]] == {False} && Max[ DigitCount[#]]==1&] (* Harvey P. Dale, Dec 30 2012 *)

is(k) = isprime(k) && setintersect([0, 1, 4, 6, 8, 9], v=vecsort(digits(k))) == v; \\ Jinyuan Wang, Mar 27 2020

Entries checked by R. J. Mathar, Mar 29 2010

A179922 Primes with twelve embedded primes.

Original entry on oeis.org

113171, 113173, 113797, 123719, 153137, 179719, 199739, 213173, 229373, 231197, 233113, 233713, 236779, 237331, 237619, 237971, 241973, 259397, 317971, 327193, 343373, 353173, 361373, 372719, 373379, 382373, 432713, 519733, 521137, 521317

Offset: 1

Robert G. Wilson v, Aug 01 2010

A079066(a(n)) = 12.

Cf. A039996, A079397, A033274, A034844, A092621, A179909 - A179919, A033274.

import Data.List (elemIndices)
a179922 n = a179922_list !! (n-1)
a179922_list = map (a000040 . (+ 1)) $ elemIndices 12 a079066_list
-- Reinhard Zumkeller, Jul 19 2011

f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 43150, f@# == 13 &]

A152426 Primes that have both prime digits (2,3,5,7) and nonprime digits (0,1,4,6,8,9).

Original entry on oeis.org

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 193, 197, 211, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 347, 349, 359, 367, 379

Offset: 1

Omar E. Pol, Dec 03 2008

See also A152427, a subsequence without zeros.

Cf. A019546, A034844, A087363, A092621, A092626, A152312, A152313, A152427.

okQ[n_] := Module[{d=Union[IntegerDigits[n]]}, Length[Intersection[d, {2,3,5,7}]]>0 && Length[Intersection[d, {0,1,4,6,8,9}]]>0]; Select[Prime[Range[100]], okQ] (* T. D. Noe, Jan 20 2011 *)

Edited by Omar E. Pol, Jul 04 2009, Jan 20 2011

Definition clarified by N. J. A. Sloane, Jul 05 2009

A152427 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9).

Original entry on oeis.org

13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 193, 197, 211, 229, 239, 241, 251, 263, 269, 271, 281, 283, 293, 311, 313, 317, 331, 347, 349, 359, 367, 379, 383, 389, 397, 421, 431, 433, 439

Offset: 1

Omar E. Pol, Dec 03 2008

A000040 \ A034844 \ A019546.

Cf. A018252.

Cf. A018252, A019546, A034844, A087363, A092621, A092626, A152312, A152313, A152426.

okQ[n_] := Module[{d = Union[IntegerDigits[n]]}, Length[Intersection[d, {2, 3, 5, 7}]] > 0 && Length[Intersection[d, {1, 4, 6, 8, 9}]] > 0]; Select[Prime[Range[100]], okQ] (* T. D. Noe, Jan 21 2011 *)
pdQ[n_]:=Module[{idn=Select[IntegerDigits[n],#!=0&]},Count[idn,?PrimeQ]>0&&Count[idn,?(!PrimeQ[#]&)]>0]; Select[Prime[Range[100]],pdQ] (* Harvey P. Dale, Jan 31 2013 *)

a(n) ~ n log n

Corrected and extended by Harvey P. Dale, Jan 31 2013

A179910 Primes with two embedded primes.

Original entry on oeis.org

23, 37, 53, 73, 127, 139, 157, 167, 193, 211, 227, 229, 241, 251, 263, 277, 307, 331, 383, 389, 419, 433, 439, 443, 457, 467, 503, 521, 541, 557, 563, 577, 587, 599, 619, 631, 643, 647, 659, 677, 683, 727, 751, 757, 761, 827, 829, 839, 857, 859, 883, 929

Offset: 1

Robert G. Wilson v, Aug 01 2010

It appears that p having n embedded primes means that the set of prime integers generated by contiguous proper substrings of p has size n.

A079066(a(n)) = 2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A039996, A079397, A033274, A034844, A092621, A179909 - A179919, A033274.

import Data.List (elemIndices)
a179910 n = a179910_list !! (n-1)
a179910_list = map (a000040 . (+ 1)) $ elemIndices 2 a079066_list
-- Reinhard Zumkeller, Jul 19 2011

f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 160, f@# == 3 &]
Select[ Prime@ Range@ 160, Function[ n, Length@ Select[ Union[ FromDigits /@ (Flatten[ Table[ Partition[#, k, 1], {k, Length@ # - 1}], 1] &)@ IntegerDigits@ n], PrimeQ]]@ # == 2 &] (* Michael Somos, Jan 13 2011 *)

cp's OEIS Frontend

A083185 Palindromic primes using only nonprime digits (0,1,4,6,8,9).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A092624 Numbers with exactly two prime digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

A092625 Numbers with exactly three prime digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

A152312 Primes without odd prime digits.

Views

Author

Keywords

Crossrefs

A179335 a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python

A155024 Primes with distinct nonprime digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A179922 Primes with twelve embedded primes.

Views

Author

Keywords

Comments

Crossrefs

Programs

Haskell

Mathematica

A152426 Primes that have both prime digits (2,3,5,7) and nonprime digits (0,1,4,6,8,9).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A152427 Primes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9).

Views