A258437 -id:A258437 - cp's OEIS frontend

A258383 Run lengths of consecutive identical terms in A062234.

2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1

Offset: 1

Reinhard Zumkeller, May 31 2015

nonn

a(A258437(n)) = n and a(m) != n for m < A258437(n). [Because of recent changes that were made to A258437, this comment may now need to be changed. - N. J. A. Sloane, Oct 31 2024]

			See A258432.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A062234, A258432, A258437.

import Data.List (group)
a258383 n = a258383_list !! (n-1)
a258383_list = map length $ group a062234_list

Map[Length, Most[Split[ListConvolve[{-1, 2}, Prime[Range[200]]]]]] (* Paolo Xausa, Oct 30 2024 *)

A257762 Numbers n with property that A062234(n) = A062234(n+1).

Original entry on oeis.org

1, 3, 5, 7, 13, 26, 28, 43, 49, 64, 69, 78, 89, 93, 96, 116, 131, 134, 142, 148, 152, 155, 167, 182, 202, 206, 212, 225, 231, 234, 236, 238, 247, 253, 258, 281, 286, 302, 303, 311, 313, 330, 332, 333, 334, 336, 337, 356, 362, 384, 385, 390, 435, 438, 455, 458, 484, 492, 512, 516

Offset: 1

Zak Seidov, May 07 2015

nonn

Numbers n with property that 2*prime(n)-prime(n+1) = 2*prime(n+1)-prime(n+2), or 2*prime(n)+prime(n+2) = 3*prime(n+1).
Numbers n with property that 2*A001223(n) = A001223(n+1). - Gionata Neri, May 22 2015
a(n) = A258432(m), where m such that A258383(m) = 2. - Reinhard Zumkeller, May 31 2015

			a(1) = A258437(A258432(2)) = 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A258383, A258432, A258437, A258469, A257762, A258449, A257892, A257951.

a257762 n = a257762_list !! (n-1)
a257762_list = map a258432 $ filter ((== 2) . a258383) [1..]
-- Reinhard Zumkeller, May 31 2015

[n: n in [0..600] | 2*NthPrime(n)-NthPrime(n+1) eq 2*NthPrime(n+1)-NthPrime(n+2)]; // Vincenzo Librandi, May 12 2015

Primes:= select(isprime,[2,(2*i+1 $ i=1..10^4)]):
Gaps:= Primes[2..-1] - Primes[1..-2]:
G2:= Gaps[2..-1] - 2*Gaps[1..-2]:
ListTools:-SearchAll(0,G2); # Robert Israel, May 22 2015

Select[Range@ 600, 2 Prime[#] - Prime[# + 1] == 2 Prime[# + 1] - Prime[# + 2] &] (* Michael De Vlieger, May 11 2015 *)

A257951 Numbers n with property that A062234(n)=A062234(n+1)=A062234(n+2)=A062234(n+3)=A062234(n+4).

Original entry on oeis.org

465460, 672832, 829363, 891802, 919088, 1703659, 2656715, 2669971, 3035410, 3223041, 3585960, 3608292, 3636024, 4047253, 4058989, 4232549, 4591286, 4785400, 4797700, 5054313, 5120280, 5599321, 5872369, 6089675, 6541163, 6963642, 7957852, 8234393, 9069087, 9082140, 9312431

Offset: 1

Zak Seidov, May 14 2015

nonn

a(n) = A258432(m), where m such that A258383(m) = 5. - Reinhard Zumkeller, May 31 2015

			For k=465460..465464, 2*prime(k)-prime(k+1)=6824895.
a(1) = A258437(A258432(5)) = 465460.

Subsequence of A257892, A257762 and A062234.

Cf. A258383, A258432, A258437, A258469, A258449, A257951.

a257951 n = a257951_list !! (n-1)
a257951_list = map a258432 $ filter ((== 5) . a258383) [1..]
-- Reinhard Zumkeller, May 31 2015

More terms from Zak Seidov, Jul 29 2015

A257892 Numbers n with property that A062234(n) = A062234(n+1) = A062234(n+2) = A062234(n+3).

Original entry on oeis.org

332, 878, 1999, 3949, 4524, 5953, 6576, 8676, 10068, 11840, 17107, 17208, 19034, 19525, 46771, 46828, 52767, 54567, 54927, 56879, 58695, 61748, 65926, 77168, 77676, 79722, 92775, 92823, 96099, 101607, 111007, 136141, 160095, 160418, 173404

Offset: 1

Zak Seidov, May 14 2015

nonn

a(n) = A258432(m), where m such that A258383(m) = 4. - Reinhard Zumkeller, May 31 2015

			a(1) = A258437(A258432(4)) = 332. - _Reinhard Zumkeller_, May 31 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..110

Subsequence of A257762 and A062234.

Cf. A258383, A258432, A258437, A258469, A258449, A257892, A257951.

a257892 n = a257892_list !! (n-1)
a257892_list = map a258432 $ filter ((== 4) . a258383) [1..]
-- Reinhard Zumkeller, May 31 2015

d(k) = 2*prime(k)-prime(k+1);
isok(n) = (d(n) == d(n+1)) && (d(n+1) == d(n+2)) && (d(n+2) == d(n+3)); \\ Michel Marcus, May 29 2015

use Math::Prime::Util::PrimeArray; tie my @prime,"Math::Prime::Util::PrimeArray"; sub d { 2*$prime[$[0]-1] - $prime[$[0]] } for (1..1e6) { my $dk=d($); say if d($+1)==$dk && d($+2)==$dk && d($+3)==$dk } # Dana Jacobsen, May 31 2015

use ntheory ":all"; { my @prime; sub d { 2*$prime[$[0]-1] - $prime[$[0]] } sub list { my $n=shift; @prime=@{primes(nth_prime($n+5))}; my @d=map{d($)}1..4; my @list; for (1..$n) { push @list,$ if $d[0]==$d[1] && $d[0]==$d[2] && $d[0]==$d[3]; @d=(@d[1..3],d($+4)) } @list; } } say join ", ",list(1e6); # _Dana Jacobsen, May 31 2015

A258449 Numbers n such that A062234(n) = A062234(n+1) = A062234(n+2).

Original entry on oeis.org

302, 336, 384, 805, 1016, 1043, 1963, 2201, 2364, 2398, 2495, 2506, 2528, 2574, 2683, 2734, 3208, 4267, 4561, 4659, 5234, 5415, 5525, 5620, 5759, 5903, 6044, 6258, 6543, 7737, 7928, 8019, 8039, 8115, 8521, 8717, 8833, 9056, 9165, 9379, 9730, 10302, 10495

Offset: 1

Reinhard Zumkeller, May 31 2015

nonn

a(n) = A258432(m), where m such that A258383(m) = 3.

			a(1) = A258437(A258432(3)) = 302.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A062234, A258383, A258432, A258437, A258469, A257762, A257892, A257951.

a258449 n = a258449_list !! (n-1)
a258449_list = map a258432 $ filter ((== 3) . a258383) [1..]

A258469 Numbers m such that A062234(m) != A062234(m+1).

Original entry on oeis.org

9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 91

Offset: 1

Reinhard Zumkeller, May 31 2015

nonn

a(n) = A258432(m), where m such that A258383(m) = 1.

			a(1) = A258437(A258432(1)) = 9.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A062234, A258383, A258432, A258437, A257762, A258449, A257892, A257951.

a258469 n = a258469_list !! (n-1)
a258469_list = map a258432 $ filter ((== 1) . a258383) [1..]

cp's OEIS Frontend

A258383 Run lengths of consecutive identical terms in A062234.

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A257762 Numbers n with property that A062234(n) = A062234(n+1).

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A257951 Numbers n with property that A062234(n)=A062234(n+1)=A062234(n+2)=A062234(n+3)=A062234(n+4).

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A257892 Numbers n with property that A062234(n) = A062234(n+1) = A062234(n+2) = A062234(n+3).

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A258449 Numbers n such that A062234(n) = A062234(n+1) = A062234(n+2).

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A258469 Numbers m such that A062234(m) != A062234(m+1).

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