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.

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A052234 Primes p from A031924 such that A052180(primepi(p)) = 17.

Original entry on oeis.org

727, 1033, 1747, 2837, 4093, 5387, 5897, 6337, 7121, 7867, 8887, 9467, 10723, 11437, 13751, 15077, 15313, 15791, 16097, 16333, 17047, 17117, 17321, 19597, 20177, 21401, 22147, 23167, 28541, 28573, 30307, 31327, 33641, 41017, 41597
Offset: 1

Views

Author

Labos Elemer, Feb 01 2000

Keywords

Crossrefs

A052235 Primes p from A031924 such that A052180(primepi(p)) = 19.

Original entry on oeis.org

433, 587, 1117, 2411, 4007, 4993, 5107, 5147, 5563, 6703, 6857, 6971, 7541, 10847, 12973, 14951, 18787, 21221, 24373, 24527, 27947, 29201, 30341, 30643, 30757, 36913, 37483, 38321, 39877, 40487, 42767, 43451, 45007, 46301, 47287, 48883, 49037
Offset: 1

Views

Author

Labos Elemer, Feb 01 2000

Keywords

Crossrefs

Programs

  • Mathematica
    Reap[For[p = 23, p < 50000, p = q, q = NextPrime[p]; If[q == p + 6 && Max[ FactorInteger[#][[1, 1]]& /@ Range[p+1, q-1]] == 19, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jan 29 2018 *)

A052236 Primes p from A031924 such that A052180(primepi(p)) = 29.

Original entry on oeis.org

1187, 1361, 2287, 3797, 4723, 5711, 7451, 10061, 10987, 12497, 17021, 18587, 20327, 22067, 25603, 26417, 32563, 41263, 41381, 43991, 50833, 53617, 55997, 60521, 64871, 71713, 77977, 81457, 84011, 87317, 87547, 89983, 90971, 98801
Offset: 1

Views

Author

Labos Elemer, Feb 01 2000

Keywords

Crossrefs

A052237 Primes p from A031924 such that A052180(primepi(p)) = 31.

Original entry on oeis.org

1453, 3313, 5981, 6911, 8707, 15467, 22721, 25447, 25633, 26627, 29167, 30097, 31957, 42187, 42373, 42437, 46093, 48017, 48947, 49627, 51673, 52667, 58061, 59113, 62897, 68477, 74923, 78643, 78707, 105613, 106357, 107351, 108217
Offset: 1

Views

Author

Labos Elemer, Feb 01 2000

Keywords

Crossrefs

Programs

  • Mathematica
    f[p_] := Max[FactorInteger[#][[1, 1]] & /@ Range[ p+1, NextPrime[p] - 1]]; Select[Prime@ Range@ 10300, NextPrime[#] == # + 6 && f[#] == 31 &] (* Giovanni Resta, May 30 2018 *)

A052238 Primes p from A031924 such that A052180(p) = 23.

Original entry on oeis.org

941, 1217, 1907, 3607, 4391, 6047, 6367, 8117, 8713, 9127, 9221, 10093, 10601, 11981, 12577, 14741, 19571, 19753, 23203, 23893, 24677, 25367, 28723, 29921, 36131, 36313, 39857, 41143, 42937, 51907, 52183, 52691, 54667, 55633, 58211
Offset: 1

Views

Author

Labos Elemer, Feb 01 2000

Keywords

Crossrefs

A355161 Primes p such that p - prevprime(p) is not a power of 2.

Original entry on oeis.org

29, 37, 53, 59, 67, 79, 89, 127, 137, 149, 157, 163, 173, 179, 191, 211, 223, 239, 251, 257, 263, 269, 277, 293, 307, 331, 337, 347, 359, 373, 379, 389, 419, 431, 439, 449, 479, 509, 521, 541, 547, 557, 563, 569, 577, 587, 593, 599, 607, 613
Offset: 1

Views

Author

Reed Michael Upson, Jun 21 2022

Keywords

Comments

A130796(n) is prevprime(p).
A031925 and A031931 are subsequences, as 6 and 12 are not powers of 2.

Crossrefs

Programs

  • Mathematica
    Select[Prime[Range[2, 120]], (d = # - NextPrime[#, -1]) != 2^IntegerExponent[d, 2] &] (* Amiram Eldar, Jun 22 2022 *)
  • PARI
    isp2(n) = my(p); (n==1) || (isprimepower(n, &p) && (p==2)); \\ A000079
    isok(p) = isprime(p) && !isp2(p-precprime(p-1)) \\ Michel Marcus, Jun 22 2022
    
  • Python
    from itertools import islice, count
    from sympy import prime, prevprime
    def A355161_gen(): # generator of terms
        return filter(lambda n:((~(m:=n-prevprime(n))+1)&m)-m, (prime(n) for n in count(2)))
    A355161_list = list(islice(A355161_gen(),30)) # Chai Wah Wu, Aug 23 2022

Formula

a(n) = A151800(A130796(n)).
Previous Showing 21-26 of 26 results.