A215035 -id:A215035 - cp's OEIS frontend

A215029 To get a(n), start with m=n, let p = largest prime < m, set m = m-p if m>0, or m=m+p if m <= 0; repeat until p=2 has been processed; set a(n) = m.

0, 1, 2, 1, -1, 0, 0, 1, 1, 2, -1, 0, 0, 1, 1, 2, -1, 0, 0, 1, 1, 2, -1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, -1, 0, 1, 2, 0, 1, -1, 0, 1, 2, 0, 1, 0, 1, 0, 1, -1, 0, 1, 2, -1, 0, 0, 1, 1, 2, -1, 0, 1, 2, 0, 1, 0, 1, -1, 0, 0, 1, 0, 1, 0, 1, 1, 2, -1, 0, 0, 1, 0, 1, 0, 1, 1, 2, -1, 0, 1, 2, -1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, -1, 0, 0, 1, 0, 1, 1

Offset: 0

N. J. A. Sloane, Aug 05 2012

sign

Antti Karttunen, Table of n, a(n) for n = 0..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..100003
StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215030-A215035, A214912.

f:=proc(n) local m,a,i,p;
if n <= 2 then RETURN(n); fi;
m:=n; a:=n;
for i from 1 to n do
p:=prevprime(m);
if a>0 then a:=a-p else a:=a+p; fi;
m:=p;
if m <= 2 then RETURN(a); fi;
od;
# should never reach here
print("ERROR");
end;
[seq(f(i),i=0..120)];

A215029(n) = if(n<=2,n,my(mp=precprime(n-1),d=n); while(mp>0, if(d>0, d -= mp, d += mp); mp = precprime(mp-1)); (d)); \\ Antti Karttunen, Nov 28 2018

A214912 Primes p such that A215029(p) = 0.

Original entry on oeis.org

5, 11, 17, 23, 59, 73, 83, 97, 109, 137, 157, 167, 191, 197, 211, 227, 233, 257, 277, 307, 331, 379, 419, 439, 509, 547, 571, 599, 643, 661, 677, 691, 709, 727, 797, 823, 853, 877, 947, 977, 991, 1009, 1031, 1051, 1087, 1103, 1117, 1153, 1171, 1229, 1259, 1289, 1303, 1319, 1367, 1381, 1453, 1471, 1489, 1597, 1621, 1663, 1709, 1753, 1867, 1879, 1901, 1933

Offset: 1

N.Harishankar, Jul 29 2012

If p is in this sequence then p is a linear combination of all smaller primes taken with coefficients either 1 or -1. (The converse is not true.)

			5=3+2 is a member, so is 11=7+5-3+2.

StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215029-A215035.

Edited and extended by N. J. A. Sloane, Aug 05 2012

A215030 a(n) = A215029(A000040(n)), where A000040(n) is the n-th prime.

Original entry on oeis.org

2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, 1, 2

Offset: 1

N. J. A. Sloane, Aug 05 2012

nonn

For primes whose value is 0, see A214912; for value 1 see A031215; and for value 2 see A215031.

Antti Karttunen, Table of n, a(n) for n = 1..10000
StackExchange, A prime number pattern, Jul 29 2012.

Cf. A000040, A215029, A214912, A031215, A215031, A215032, A215033, A215034, A215035.

A215029(n) = if(n<=2,n,my(mp=precprime(n-1),d=n); while(mp>0, if(d>0, d -= mp, d += mp); mp = precprime(mp-1)); (d));
A215030(n) = A215029(prime(n)); \\ Antti Karttunen, Nov 28 2018

A215031 Primes p such that A215029(p) = 2.

Original entry on oeis.org

2, 31, 41, 47, 67, 103, 127, 149, 179, 241, 269, 283, 313, 347, 353, 367, 389, 401, 431, 449, 461, 467, 487, 499, 523, 563, 587, 607, 617, 631, 653, 739, 751, 761, 773, 811, 829, 859, 883, 907, 919, 937, 967, 1019, 1039, 1063, 1093, 1129, 1187, 1201, 1217, 1237, 1279, 1297, 1327, 1409, 1427, 1433, 1447, 1483, 1499, 1523, 1543, 1553, 1567, 1579, 1607, 1613, 1637

Offset: 1

N. J. A. Sloane, Aug 05 2012

nonn

StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215029-A215035, A214912.

A215032 Numbers n such that A215029(n) = -1.

Original entry on oeis.org

4, 10, 16, 22, 38, 44, 54, 58, 64, 72, 82, 92, 96, 108, 116, 120, 124, 132, 136, 142, 146, 152, 156, 166, 176, 182, 186, 190, 196, 202, 206, 210, 226, 232, 252, 256, 266, 272, 276, 294, 298, 302, 306, 318, 322, 326, 330, 340, 344, 350, 360, 364, 374, 378, 386, 398, 410, 414, 418, 424, 428, 434, 438, 446, 458, 464, 480, 484, 492, 496, 504, 508, 542, 546, 560

Offset: 1

N. J. A. Sloane, Aug 05 2012

nonn

All terms are composite.

StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215029-A215035.

A215033 Numbers n such that A215029(n) = 0.

Original entry on oeis.org

0, 5, 6, 11, 12, 17, 18, 23, 24, 26, 28, 32, 34, 36, 39, 42, 45, 48, 50, 52, 55, 59, 60, 65, 68, 70, 73, 74, 76, 78, 83, 84, 86, 88, 93, 97, 98, 100, 104, 106, 109, 110, 112, 117, 121, 125, 128, 130, 133, 137, 138, 143, 147, 150, 153, 157, 158, 160, 162, 167, 168, 170, 172, 177, 180, 183, 187, 191, 192, 197, 198, 203, 207, 211, 212, 214, 216, 218, 220, 222, 227

Offset: 1

N. J. A. Sloane, Aug 05 2012

nonn

StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215029-A215035. A214912 is a subsequence.

A215034 Numbers n such that A215029(n) = 1.

Original entry on oeis.org

1, 3, 7, 8, 13, 14, 19, 20, 25, 27, 29, 30, 33, 35, 37, 40, 43, 46, 49, 51, 53, 56, 61, 62, 66, 69, 71, 75, 77, 79, 80, 85, 87, 89, 90, 94, 99, 101, 102, 105, 107, 111, 113, 114, 118, 122, 126, 129, 131, 134, 139, 140, 144, 148, 151, 154, 159, 161, 163, 164, 169, 171, 173, 174, 178, 181, 184, 188, 193, 194, 199, 200, 204, 208, 213, 215, 217, 219, 221, 223, 224

Offset: 1

N. J. A. Sloane, Aug 05 2012

nonn

StackExchange, A prime number pattern, Jul 29 2012.

Cf. A215029-A215035. A031215 is a subsequence.

cp's OEIS Frontend

A215029 To get a(n), start with m=n, let p = largest prime < m, set m = m-p if m>0, or m=m+p if m <= 0; repeat until p=2 has been processed; set a(n) = m.

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A214912 Primes p such that A215029(p) = 0.

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A215030 a(n) = A215029(A000040(n)), where A000040(n) is the n-th prime.

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A215031 Primes p such that A215029(p) = 2.

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A215032 Numbers n such that A215029(n) = -1.

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A215033 Numbers n such that A215029(n) = 0.

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A215034 Numbers n such that A215029(n) = 1.

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