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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A377782 First-differences of A031218(n) = greatest number <= n that is 1 or a prime-power.

Original entry on oeis.org

1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 0, 3, 1, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Gus Wiseman, Nov 16 2024

Keywords

Comments

Note 1 is a power of a prime (A000961) but not a prime-power (A246655).

Crossrefs

Positions of 1 are A006549.
Positions of 0 are A080765 = A024619 - 1, complement A181062 = A000961 - 1.
Positions of 2 are A120432 (except initial terms).
Sorted positions of first appearances appear to include A167236 - 1.
Positions of terms > 1 are A373677.
The restriction to primes minus 1 is A377289.
Below, A (B) indicates that A is the first-differences of B:
- This sequence is A377782 (A031218), which has restriction to primes A065514 (A377781).
- The opposite is A377780 (A000015), restriction A377703 (A345531).
- For nonsquarefree we have A378036 (A378033), opposite A378039 (A120327).
- For squarefree we have A378085 (A112925), restriction A378038 (A070321).
A000040 lists the primes, differences A001223.
A000961 and A246655 list prime-powers, differences A057820.
A024619 lists the non-prime-powers, differences A375735, seconds A376599.
A361102 lists the non-powers of primes, differences A375708.
A378034 gives differences of A378032 (restriction of A378033).
Prime-powers between primes: A053607, A080101, A366833, A377057, A377286, A377287.
Cf. A053289, A343249, A375706, A377281, A377282.

Programs

  • Mathematica
    Differences[Table[NestWhile[#-1&,n,#>1&&!PrimePowerQ[#]&],{n,100}]]

A121492 Gaps associated with A002540(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 20, 22, 30, 32, 34, 36, 44, 52, 72, 86, 96, 112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282, 288, 292, 320, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490, 500, 514, 516, 532, 534, 540, 582, 588, 602
Offset: 1

Views

Author

Lekraj Beedassy, Aug 03 2006

Keywords

Comments

Record gaps between prime powers (A000961) [Michael B. Porter, Nov 01 2009].

Examples

			6 is in the sequence since 53 and 59 are consecutive prime powers and no smaller pair of consecutive prime powers differ by 6 or more. [From _Michael B. Porter_, Nov 03 2009]

Links

  • Jan Kristian Haugland, Table of n, a(n) for n = 1..87 (terms 1..79 from _Donovan Johnson_). The extra terms are copied from A005250 as the associated prime gaps do not contain any prime powers.

Crossrefs

Cf. A002540, A167236, A057820, A000961 [Michael B. Porter, Nov 01 2009]
start of gap: A002540, end of gap: A167236, gaps: A057820 [From Michael B. Porter, Nov 03 2009]

Programs

  • PARI
    isA000961(n) = (omega(n) == 1 || n == 1)
d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(d); d_max=d);n_prev=n)) /* Michael B. Porter, Nov 01 2009 */

Extensions

Second term corrected. a(20)-a(79) and b-file from Donovan Johnson, Nov 14 2008
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