cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A344626 Primes p such that exactly two numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

13, 17, 31, 37, 71, 73, 79, 97, 101, 103, 107, 127, 149, 157, 163, 173, 181, 191, 271, 277, 307, 313, 317, 331, 359, 367, 379, 397, 419, 479, 491, 571, 577, 593, 617, 631, 673, 701, 709, 727, 739, 757, 761, 787, 797, 811, 839, 877, 907, 911, 937, 941, 947, 977
Offset: 1

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Author

Felix Fröhlich, May 25 2021

Keywords

Links

Crossrefs

Cf. A270083. Row 2 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Programs

  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==2, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

A344627 Primes p such that exactly three numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1031, 1091, 1097, 1103, 1109, 1123, 1181, 1213, 1231, 1279, 1297, 1301, 1319, 1327, 1579, 1777, 1811, 1873, 1913, 1949, 1951, 1979, 1987, 1993, 2131, 2311, 2377, 2399, 2713, 2791, 2939, 2971, 3011
Offset: 1

Views

Author

Felix Fröhlich, May 25 2021

Keywords

Links

Crossrefs

Cf. A270083. Row 3 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Programs

  • Mathematica
    Select[Prime[Range[500]],Total[Boole[PrimeQ[FromDigits/@ Table[ RotateRight[ IntegerDigits[#],n],{n,IntegerLength[#]}]]]]==3&] (* Harvey P. Dale, Mar 30 2023 *)
  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==3, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

A344628 Primes p such that exactly four numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11393, 11701, 11717, 11743, 13177, 13931, 13997, 16993, 17011, 17117, 17431, 17539, 17713, 19717, 19997, 21737, 23339, 23773, 30197, 31139, 31699, 31771, 32377, 33923, 37217, 38197, 39233, 39499, 39799, 39971
Offset: 1

Views

Author

Felix Fröhlich, May 25 2021

Keywords

Links

Crossrefs

Cf. A270083. Row 4 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344629 (k=5), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Programs

  • Mathematica
    Select[Prime[Range[4500]],Count[FromDigits/@Table[RotateRight[IntegerDigits[#],d],{d,IntegerLength[ #]}],?PrimeQ]==4&] (* _Harvey P. Dale, Aug 31 2024 *)
  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==4, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

A344629 Primes p such that exactly five numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 103391, 103997, 107119, 110339, 111893, 111919, 113123, 113177, 113983, 114997, 117133, 117319, 117353, 117701, 118931, 119107, 119179, 119191, 119699, 123113, 127733, 129919, 131231, 131771
Offset: 1

Views

Author

Felix Fröhlich, May 25 2021

Keywords

Links

Crossrefs

Cf. A270083. Row 5 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344630 (k=6), A344631 (k=7), A344632 (k=8).

Programs

  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==5, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

A344630 Primes p such that exactly six numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

193939, 199933, 319993, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331, 1313999, 1317727, 1399913, 1731893, 1743737, 1772713, 1893173, 1977779, 2713177, 3139991, 3173189, 3177271, 3189317, 3717437, 4373717, 7174373, 7271317, 7318931
Offset: 1

Views

Author

Felix Fröhlich, May 25 2021

Keywords

Links

Crossrefs

Cf. A270083. Row 6 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344631 (k=7), A344632 (k=8).

Programs

  • Mathematica
    Select[Prime[Range[500000]],Total[Boole[PrimeQ[FromDigits/@Table[RotateRight[IntegerDigits[#],n],{n,0,IntegerLength[ #]-1}]]]]==6&] (* Harvey P. Dale, Sep 22 2024 *)
  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==6, 1, 0)
forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

A344632 Primes p such that exactly eight numbers among all circular permutations of the digits of p are prime.

Original entry on oeis.org

119139133, 133119139, 139133119, 191391331, 311913913, 331191391, 913311913, 913913311, 1013517313, 1033939939, 1039191919, 1112795317, 1113194339, 1117923797, 1127953171, 1131943391, 1139937913, 1173917197, 1179237971, 1279531711, 1310135173, 1311399379
Offset: 1

Views

Author

Felix Fröhlich, May 25 2021

Keywords

Crossrefs

Cf. A270083. Row 8 of A317716.
Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344629 (k=5), A344630 (k=6), A344631 (k=7).

Programs

  • PARI
    rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
eva(n) = subst(Pol(n), x, 10)
is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==8, 1, 0)
forprime(p=1, , if(is(p), print1(p, ", ")))
Showing 1-6 of 6 results.

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