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.

A182178 Beginning with 1, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 9, 20, 21, 11, 12, 14, 16, 50, 23, 25, 29, 41, 43, 47, 49, 83, 85, 61, 65, 67, 411, 111, 112, 30, 32, 34, 38, 52, 56, 58, 92, 94, 70, 74, 76, 114, 98, 302, 116, 120, 202, 121, 123, 89, 203, 205, 207, 412, 125, 211, 129, 212, 141, 143
Offset: 1

Views

Author

Jim Nastos and Eric Angelini, Apr 16 2012

Keywords

Comments

See A219110 for the numbers which do not occur in this sequence. See A219250 for the analog when "sum" is replaced with "absolute difference", and A219248-A219251 for related sequences. - M. F. Hasler, Apr 11 2013

Examples

			20 follows 9 since 9+2 and 2+0 is prime, and no number less than 20 (not already in the sequence) satisfies the stated property.

Links

Crossrefs

Cf. A182175, A182177.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = For[id = IntegerDigits[a[n-1]]; k = 1, True, k++, If[FreeQ[Array[a, n-1], k], dd = Join[id, IntegerDigits[k]]; If[And @@ PrimeQ /@ Plus @@@ Transpose[{Most[dd], Rest[dd]}], Return[k]]]]; Array[a, 62] (* Jean-François Alcover, Apr 17 2013 *)
  • PARI
    A182178_vec={(n, a=[1], u=0)->while(#aM. F. Hasler, Apr 11 2013

A219248 Numbers such that the absolute difference of any two adjacent (decimal) digits is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 18, 20, 24, 25, 27, 29, 30, 31, 35, 36, 38, 41, 42, 46, 47, 49, 50, 52, 53, 57, 58, 61, 63, 64, 68, 69, 70, 72, 74, 75, 79, 81, 83, 85, 86, 92, 94, 96, 97, 130, 131, 135, 136, 138, 141, 142, 146, 147, 149, 161, 163, 164
Offset: 1

Views

Author

M. F. Hasler, Apr 12 2013

Keywords

Comments

Numbers which may (and do) occur in A219250 and A219249 (union {0}).
This is to A219250 and A219249 what A182175 is to A182177 and A182178.

Links

Programs

  • Mathematica
    Select[Range[0,200],And@@PrimeQ[Abs[Differences[IntegerDigits[#]]]]&] (* Harvey P. Dale, Jun 06 2014 *)
  • PARI
    is_A219248(n)={!for(i=2,#n=digits(n),isprime(abs(n[i-1]-n[i]))||return)}
  • Python
    def ok(n):
    d = list(map(int, str(n)))
    return all(abs(d[i]-d[i-1]) in {2,3,5,7} for i in range(1, len(d)))
print([k for k in range(164) if ok(k)]) # Michael S. Branicky, Sep 11 2024
  • Python
    from itertools import count, islice
def A219248gen(seed=None): # generator of terms
    nxt = {None:"123456789", "0":"2357", "1":"3468", "2":"04579",
        "3":"01568", "4":"12679", "5":"02378", "6":"13489",
        "7":"02459", "8":"1356", "9":"2467"}
    def bgen(d, seed=None):
        if d == 0: yield tuple(); return
        yield from ((i,)+t for i in nxt[seed] for t in bgen(d-1, seed=i))
    yield 0
    for d in count(1):
        yield from (int("".join(t)) for t in bgen(d, seed=seed))
print(list(islice(A219248gen(), 65))) # Michael S. Branicky, Sep 11 2024

A182177 Beginning with 0, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

Original entry on oeis.org

0, 2, 1, 4, 3, 8, 5, 6, 7, 41, 11, 12, 9, 20, 21, 14, 16, 50, 23, 25, 29, 43, 47, 49, 83, 85, 61, 65, 67, 411, 111, 112, 30, 32, 34, 38, 52, 56, 58, 92, 94, 70, 74, 76, 114, 98, 302, 116, 120, 202, 121, 123, 89, 203, 205, 207, 412, 125, 211, 129, 212, 141, 143, 214, 147, 414, 149, 216, 161, 165, 230, 232, 167, 416, 502, 303, 234, 305, 238, 307, 430, 250, 252, 320, 256, 503, 258, 321, 292, 323, 294, 325, 298, 329, 432, 341, 434, 343, 438, 347, 470, 349
Offset: 1

Views

Author

Jim Nastos and Eric Angelini, Apr 16 2012

Keywords

Comments

A219250 is the analog of this sequence, replacing "sum" by "absolute difference". A219249 is the same analog for A182178. A219248 is the analog of A182175 and A219251 corresponds to A219110 = terms which do not occur in this sequence, i.e., the complement of its range. - M. F. Hasler, Apr 12 2013

Examples

			41 appears after 7 because 7+4 is prime and 4+1 is prime, and no other number less than 41 (not already in the sequence) satisfies this property. Example: 11 does not directly follow 7 since 7+1 is not prime.

Crossrefs

Cf. A182175.

Programs

  • PARI
    A182177_vec={(n, a=[0], u=0)->while(#aM. F. Hasler, Apr 11 2013

A219249 Lexicographically earliest sequence of positive integers such that the absolute difference of any two adjacent digits is prime.

Original entry on oeis.org

1, 3, 5, 2, 4, 6, 8, 13, 14, 7, 9, 20, 24, 16, 18, 30, 25, 27, 29, 41, 31, 35, 36, 38, 50, 52, 42, 46, 47, 49, 61, 63, 53, 57, 58, 64, 68, 69, 70, 72, 74, 75, 79, 202, 92, 94, 96, 81, 83, 85, 86, 97, 203, 130, 205, 207, 241, 302, 413, 131, 303, 135, 242, 414, 136, 138, 141, 305, 246, 142, 416, 146, 147, 247, 249, 250
Offset: 1

Views

Author

Eric Angelini and M. F. Hasler, Apr 11 2013

Keywords

Comments

See A219250 for the version allowing nonnegative integers, i.e., starting with a(1)=0.
See A219248 for the numbers which occur in this sequence, and A219251 for the complement.

Links

Crossrefs

Cf. A182175, A182177, A182178.

Programs

  • PARI
    {A219249(n,a=[1],u=0)=while(#a

A219251 Numbers such that the absolute difference of a pair of adjacent decimal digits is not prime.

Original entry on oeis.org

10, 11, 12, 15, 17, 19, 21, 22, 23, 26, 28, 32, 33, 34, 37, 39, 40, 43, 44, 45, 48, 51, 54, 55, 56, 59, 60, 62, 65, 66, 67, 71, 73, 76, 77, 78, 80, 82, 84, 87, 88, 89, 90, 91, 93, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2013

Keywords

Comments

Complement of A219248; numbers which do not occur in A219249 and A219250; analog of what is A219110 to A182177, A182178.

Programs

  • PARI
    is_A219251(n)={for(i=2, #n=digits(n), isprime(abs(n[i-1]-n[i]))||return(1))}

A358054 Starting with 0, smallest integer not yet in the sequence such that no two neighboring digits differ by 1.

Original entry on oeis.org

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 90, 80
Offset: 0

Views

Author

Gavin Lupo and Eric Angelini, Oct 28 2022

Keywords

Comments

Integers such as 10, 12, 21, 76, 6792, and 10744 (see A082927) will not appear in the sequence as they contain adjacent digits that differ by 1. Some integers may be disallowed only temporarily; for example, if a(n) = 79, and all nonnegative integers < 79 are already in the sequence, then a(n+1) = 90, because a(n+1) must not start with an 8, as it would differ by 1 from the digit "9" in 79. Now, a(n+2) can equal 80.

Examples

			a(0) = 0.
a(1) = 2. Cannot be 1. Smallest integer that can be placed = 2.
a(2) = 4. Cannot be 1 or 3. Smallest integer that can be placed = 4.
a(3) = 1. Cannot be 3 or 5. Smallest integer that can be placed = 1.
...
(Nonnegative integers < 86, disregarding invalid integers, have already appeared.)
a(74) = 86.
a(75) = 88. Cannot be 87, as it contains adjacent digits that differ by 1. Smallest integer that can be placed = 88.
a(76) = 111. Cannot be 89, 90->99 (9 and 8 differ by 1), or 100->110 (1 and 0 are adjacent and differ by 1). Smallest integer that can be placed = 111.

Links

Crossrefs

Cf. A082927, A219250.

Programs

Showing 1-6 of 6 results.

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