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.

A122091 Numbers appearing in A122072 at least twice.

Original entry on oeis.org

199, 317, 509, 523, 619, 839, 887, 1069, 1129, 1259, 1327, 1409, 1459, 1499, 1637, 1669, 1709, 1759, 1789, 1847, 1889, 1913, 1951, 2039, 2069, 2099, 2179, 2311, 2357, 2399, 2477, 2503, 2557, 2579, 2819, 2939, 2971, 3049, 3089, 3137, 3169, 3229, 3259
Offset: 1

Views

Author

Zak Seidov, Oct 17 2006

Keywords

Comments

Necessary condition: p is followed by a prime gap of at least 12. Sufficient condition: p is followed by a prime gap of at least 20. [Charles R Greathouse IV, Feb 26 2012]

Links

Crossrefs

Cf. A122072.

Programs

Formula

a(n) ~ n log n since this sequence contains almost all primes. [Charles R Greathouse IV, Feb 26 2012]

A122384 Numbers appearing in A122072 at least three times.

Original entry on oeis.org

1129, 1327, 1669, 2179, 2477, 3137, 3229, 3469, 3739, 4177, 4297, 4759, 4831, 5119, 5237, 5351, 5449, 5591, 5749, 5953, 6397, 6491, 6737, 6917, 7079, 7129, 7253, 7369, 7759, 7963, 8329, 8389, 8467, 8893, 9067, 9349, 9439, 9551, 9973, 10009, 10039
Offset: 1

Views

Author

Zak Seidov, Oct 19 2006

Keywords

Comments

Necessary condition: p is followed by a prime gap of at least 22. Sufficient condition: p is followed by a prime gap of at least 30. [Charles R Greathouse IV, Feb 26 2012]

Links

Crossrefs

Cf. A122091, A122072.

Programs

Formula

a(n) ~ n log n since this sequence contains almost all primes. [Charles R Greathouse IV, Feb 26 2012]

A122390 Numbers appearing in A122072 at least four times.

Original entry on oeis.org

1327, 8467, 10799, 14107, 15683, 16141, 17257, 19087, 19333, 19609, 20809, 22307, 22573, 22817, 25261, 25471, 28229, 30593, 31397, 31907, 33247, 34061, 34549, 34981, 35617, 35677, 36389, 37747, 37907, 38393, 38461, 38501, 39251, 40289, 40387, 40639, 41299, 43331, 43801
Offset: 1

Views

Author

Zak Seidov, Oct 19 2006

Keywords

Comments

19609 is first term appearing in A122072 six times.
Necessary condition: p is followed by a prime gap of at least 32. Sufficient condition: p is followed by a prime gap of at least 40. [Charles R Greathouse IV, Feb 26 2012]

Links

Crossrefs

Cf. A122091, A122072.

Programs

Formula

a(n) ~ n log n since this sequence contains almost all primes. [Charles R Greathouse IV, Feb 26 2012]

Extensions

a(11)-a(39) from Charles R Greathouse IV, Feb 26 2012

A206473 First prime in A122072 that appears at least n times.

Original entry on oeis.org

7, 199, 1129, 1327, 19609, 19609, 31397, 155921, 360653, 370261, 370261, 1349533, 1357201, 1561919, 2010733, 15203977, 17051707, 17051707, 20831323, 20831323, 20831323, 47326693, 189695659, 189695659, 191912783, 436273009, 436273009, 436273009, 436273009
Offset: 1

Views

Author

Lekraj Beedassy, Feb 08 2012

Keywords

Comments

Corresponding values of n in A122072 are 1, 21, 115, 136, 1965, 1966, ....

Links

Crossrefs

Cf. A122384, A122390.

Programs

  • PARI
    a(n)=my(p=2);forprime(q=3,default(primelimit),if(q\10-p\10>=n,return(p));p=q) \\ Charles R Greathouse IV, Feb 26 2012

Extensions

a(5)-a(15) from Alois P. Heinz, Feb 08 2012
a(16)-a(36) from Charles R Greathouse IV, Feb 26 2012

A218255 Next prime after 10*n.

Original entry on oeis.org

2, 11, 23, 31, 41, 53, 61, 71, 83, 97, 101, 113, 127, 131, 149, 151, 163, 173, 181, 191, 211, 211, 223, 233, 241, 251, 263, 271, 281, 293, 307, 311, 331, 331, 347, 353, 367, 373, 383, 397, 401, 419, 421, 431, 443, 457, 461, 479, 487, 491, 503, 521, 521, 541
Offset: 0

Views

Author

Giovanni Teofilatto, Oct 24 2012

Keywords

Links

Crossrefs

Cf. A122072.

Programs

  • Mathematica
    Table[Prime[1 + PrimePi[10*n]], {n, 0, 60}] (* T. D. Noe, Oct 30 2012 *)
NextPrime/@(10 Range[0,60]) (* Harvey P. Dale, Mar 18 2018 *)

A346979 Count of the prime decimal descendants of n.

Original entry on oeis.org

83, 63, 23, 22, 23, 11, 29, 23, 3, 4, 54, 1, 9, 14, 6, 7, 3, 4, 7, 40, 0, 4, 19, 15, 8, 7, 10, 14, 5, 6, 2, 7, 0, 16, 9, 11, 12, 13, 4, 1, 34, 1, 8, 14, 5, 1, 13, 5, 5, 16, 6, 0, 9, 0, 24, 4, 6, 19, 2, 9, 25, 16, 0, 7, 4, 4, 3, 11, 2, 7, 7, 4, 1, 15, 2, 8, 8
Offset: 0

Views

Author

Ya-Ping Lu, Aug 09 2021

Keywords

Comments

The number of direct decimal descendants (i.e., decimal children) of n is A038800(n). The number of prime decimal descendants of the n-th prime is A214342(p_n). a(n) is the number of prime decimal descendants of n, which include the prime decimal children of n, the prime decimal children of the prime decimal children of n, and so on.
a(0) = Sum_{m=1..4} (A214342(m) + 1); a(1) = Sum_{m=5..8} (A214342(m) + 1).
a(A032352(m)) = 0; a(A119289(m)) = 0.
A214342 is a subset, as A214342(m) = a(prime(m)).
Conjecture 1: a(n) <= 83. Conjecture 2: lim_{n->oo} (n0/n) = 1, where n0 is the number of zero terms, a(k) = 0, for k <= n.

Examples

			a(4) = 23. The 23 prime decimal descendants of 4 are shown in the tree below.
       _____ 4__________________________
      /      |                          \
     41   ___43______________            47
    /    /   |               \             \
  419  431  433               439          479
            / \              /   \        /   \
        4337  4339         4391  4397   4793  4799
             /  |  \        |     |     /  \
        43391 43397 43399 43913 43973 47933 47939
                            |
                         439133
                            |
                        4391339

Crossrefs

Cf. A030665, A032352, A038800, A119289, A122072, A214342, A218255, A256481.

Programs

  • Mathematica
    Table[Length@Rest@Flatten[FixedPointList[(b=#;Select[Flatten[(a=#;FromDigits/@(Join[IntegerDigits@a,{#}]&/@If[b=={0},Range@9,{1,3,7,9}]))&/@b],PrimeQ])&,{n}]],{n,0,76}] (* Giorgos Kalogeropoulos, Aug 16 2021 *)
  • Python
    from sympy import isprime
def p_count(k):
    global ct; d = [2, 3, 5, 7] if k == 0 else [1, 3, 7, 9]
    for i in range(4):
        m = 10*k + d[i]
        if isprime(m): ct += 1; p_count(m)
    return ct
for n in range(100):
    ct = 0; print(p_count(n))
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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