A124177 -id:A124177 - cp's OEIS frontend

A124176 Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

0, 11, 13, 17, 18, 25, 28, 54, 55, 64, 65, 112, 121, 134, 137, 143, 148, 155, 156, 165, 166, 173, 178, 184, 187, 198, 200, 209, 211, 216, 231, 233, 234, 237, 244, 245, 270, 275, 280, 285, 314, 336, 341, 358, 363, 385, 396, 402, 407, 410, 413, 429, 431, 432

Offset: 1

Eric Angelini, Dec 04 2006

Terms computed by Barry and Theunis de Jong.

Subsequence A036301 lists fixed points of the map f = A304439. - M. F. Hasler, May 18 2018

			11 and 13 loop on themselves, but 12 doesn't:
11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11
12 -> 11 -> 13 -> 17 -> 25 -> 28 -> 18 -> 11
13 -> 17 -> 25 -> 28 -> 18 -> 11 -> 13.

Eric Angelini, Dec 04 2006, Table of n, a(n) for n = 1..172

Cf. A124177, A036301, A304439; A071648, A071649, A071650.

is(n,S=List())=until(setsearch(Set(S),n=A304439(n)),listput(S,n));n==S[1] \\ M. F. Hasler, May 18 2018

A126908 Numbers k such that 1 + k^2 + k^4 + k^6 + k^7 is prime.

Original entry on oeis.org

1, 4, 13, 15, 24, 30, 37, 40, 55, 93, 138, 139, 148, 153, 154, 159, 160, 165, 184, 195, 204, 223, 258, 303, 355, 360, 373, 459, 472, 475, 510, 519, 534, 577, 594, 607, 615, 627, 658, 672, 688, 723, 735, 739, 795, 805, 807, 817, 819, 820, 847, 874, 879, 904

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^7], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1000],PrimeQ[1+#^2+#^4+#^6+#^7]&] (* Harvey P. Dale, Jan 15 2016 *)

is(n)=isprime(1+n^2+n^4+n^6+n^7) \\ Charles R Greathouse IV, Feb 17 2017

A126916 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23 is prime.

Original entry on oeis.org

1, 2, 11, 23, 47, 64, 77, 80, 103, 251, 290, 321, 331, 335, 375, 382, 387, 403, 507, 568, 590, 594, 649, 801, 805, 828, 830, 840, 847, 854, 905, 925, 926, 959, 982, 986, 1034, 1086, 1094, 1102, 1122, 1129, 1147, 1160, 1391

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1400],PrimeQ[Total[#^Range[2,22,2]]+1+#^23]&] (* Harvey P. Dale, Oct 04 2018 *)

is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^12+n^14+n^16+n^18+n^20+n^22+n^23) \\ Charles R Greathouse IV, Feb 17 2017

A304439 Add to n the sum of its odd digits minus the sum of its even digits.

Original entry on oeis.org

0, 2, 0, 6, 0, 10, 0, 14, 0, 18, 11, 13, 11, 17, 11, 21, 11, 25, 11, 29, 18, 20, 18, 24, 18, 28, 18, 32, 18, 36, 33, 35, 33, 39, 33, 43, 33, 47, 33, 51, 36, 38, 36, 42, 36, 46, 36, 50, 36, 54, 55, 57, 55, 61, 55, 65, 55, 69, 55, 73, 54, 56, 54, 60, 54, 64, 54, 68, 54, 72

Offset: 0

M. F. Hasler, May 18 2018

Subsequence A036301 lists fixed points of this map, the first nontrivial one being 112. It is a subsequence of A124176 (and A124177) which considers iterations of this map, more precisely, numbers which are in a cyclic orbit for iterations of this map.

Cf. A304440, A071650, A071648, A071649, A036301, A124176, A124177.

soded[n_]:=Module[{idn=IntegerDigits[n]},n+Total[Select[idn,OddQ]]-Total[ Select[idn,EvenQ]]]; Array[soded,70,0] (* Harvey P. Dale, Aug 12 2021 *)

A304439(n)=n-vecsum(apply(t->t*(-1)^t,digits(n)))

a(n) = n + A071650(n).

A304440 Add to n the sum of its even digits minus the sum of its odd digits.

Original entry on oeis.org

0, 0, 4, 0, 8, 0, 12, 0, 16, 0, 9, 9, 13, 9, 17, 9, 21, 9, 25, 9, 22, 22, 26, 22, 30, 22, 34, 22, 38, 22, 27, 27, 31, 27, 35, 27, 39, 27, 43, 27, 44, 44, 48, 44, 52, 44, 56, 44, 60, 44, 45, 45, 49, 45, 53, 45, 57, 45, 61, 45, 66, 66, 70, 66, 74, 66, 78, 66, 82, 66, 63

Offset: 0

M. F. Hasler, May 18 2018

A036301 lists fixed points of this map, the first nonzero one being 112. It is also a subsequence of A124177 (and A124176) which lists numbers which are in a cyclic orbit under iterations of this map.

Cf. A304439 (variant: + even - odd digits), A071650 (odd - even digits), A071648, A071649, A036301 (fixed points), A124177, A124176.

nseo[n_]:=Module[{idn=IntegerDigits[n]},n+Total[Select[idn,EvenQ]]-Total[Select[idn,OddQ]]]; Array[nseo,80,0] (* Harvey P. Dale, Dec 26 2023 *)

A304440(n)=n+vecsum(apply(t->t*(-1)^t,digits(n)))

a(n) = n - A071650(n).

A076164 Numbers n such that sum of squares of even digits of n equals sum of squares of odd digits of n.

Original entry on oeis.org

0, 11112, 11121, 11211, 11356, 11365, 11536, 11563, 11635, 11653, 12111, 13156, 13165, 13516, 13561, 13615, 13651, 15136, 15163, 15316, 15361, 15613, 15631, 16135, 16153, 16315, 16351, 16513, 16531, 21111, 31156, 31165, 31516, 31561

Offset: 1

Zak Seidov, Nov 01 2002

The minimal number of digits in any nonzero term is 5.

Numbers such that the sum of even digits equals the sum of odd digits are listed in A036301.

			11356 is in the sequence because 1^2 + 1^2 + 3^2 + 5^2 = 6^2.

Cf. A303269, A036301 (analog without squares), A071650, A304439, A304440, A124176, A124177.

oeQ[n_]:=Module[{idn=IntegerDigits[n]},Total[Select[idn,OddQ]^2]== Total[ Select[ idn, EvenQ]^2]]; Select[Range[0,99999],oeQ] (* Harvey P. Dale, Sep 23 2011 *)

is(n)=!vecsum(apply(d->d^2*(-1)^d,digits(n))) \\ M. F. Hasler, May 18 2018

Edited and a(1) = 0 added by M. F. Hasler, May 18 2018

A126906 Smallest k such that 1 + k^(2n+1) + Sum_{j=1..n} k^(2j) is prime.

Original entry on oeis.org

1, 2, 1, 2, 1, 10, 17, 2, 1, 2, 1, 94, 122, 22, 1, 80, 1, 4, 6, 2, 1, 242, 3, 6, 5, 80, 1, 12, 1, 82, 96, 2, 7, 188, 1, 136, 69, 158, 1, 2, 1, 954, 50, 118, 1, 570, 14, 90, 45, 6, 1, 228, 38, 4, 6, 22, 1, 12, 1, 580, 86, 336, 24, 768, 1, 1170, 408, 340, 1, 896

Offset: 1

Artur Jasinski, Dec 31 2006

nonn

1 is a term if and only if number of terms in polynomial is prime.

Amiram Eldar, Table of n, a(n) for n = 1..250

Cf. A124151, A119863, A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a[n_]: = Module[{k = 1}, While[!PrimeQ[1 + k^(2*n+1) + Sum[k^(2*j), {j, 1, n}]], k++]; k]; Array[a, 30] (* Amiram Eldar, Mar 13 2020 *)

a(n) = my(k = 1); while(! isprime(1 + k^(2*n+1) + sum(j=1, n, k^(2*j))), k++); k; \\ Michel Marcus, Mar 13 2020

More terms from Amiram Eldar, Mar 13 2020

A126907 Numbers n such that 1 + n^2 + n^4 + n^5 is prime.

Original entry on oeis.org

2, 4, 6, 8, 12, 18, 32, 34, 68, 70, 78, 88, 110, 114, 116, 118, 120, 122, 132, 134, 142, 150, 172, 180, 186, 190, 210, 216, 238, 246, 254, 272, 294, 322, 362, 376, 380, 386, 388, 408, 476, 500, 502, 506, 508, 520, 530, 542, 564, 584, 588, 590, 616, 620, 632

Offset: 1

Artur Jasinski, Dec 31 2006

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^5], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[700],PrimeQ[1+#^2+#^4+#^5]&] (* Harvey P. Dale, Jun 24 2018 *)

is(n)=isprime(1+n^2+n^4+n^5) \\ Charles R Greathouse IV, Jun 13 2017

A126909 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^9 is prime.

Original entry on oeis.org

2, 18, 48, 56, 116, 120, 128, 146, 194, 198, 200, 230, 266, 278, 282, 288, 324, 362, 372, 390, 396, 420, 434, 458, 488, 576, 594, 708, 714, 728, 740, 774, 818, 830, 860, 888, 896, 912, 914, 990, 996, 1002, 1008, 1010, 1016, 1044, 1124, 1128, 1140, 1146, 1260

Offset: 1

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^9], AppendTo[a, n]], {n, 1, 1400}]; a
Select[Range[1300],PrimeQ[1+#^2+#^4+#^6+#^8+#^9]&] (* Harvey P. Dale, Apr 25 2020 *)

is(n)=isprime(1+n^2+n^4+n^6+n^8+n^9) \\ Charles R Greathouse IV, Jun 13 2017

A126910 Numbers k such that 1 + k^2 + k^4 + k^6 + k^8 + k^10 + k^11 is prime.

Original entry on oeis.org

1, 2, 3, 35, 48, 77, 97, 105, 111, 112, 122, 128, 161, 168, 175, 216, 231, 255, 271, 276, 297, 338, 361, 370, 378, 422, 485, 513, 525, 558, 622, 658, 661, 662, 667, 675, 700, 718, 725, 742, 753, 766, 770, 795, 796, 833, 875, 886, 921, 993, 1027, 1066, 1078

Offset: 1

Artur Jasinski, Dec 31 2006

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

a = {}; Do[If[PrimeQ[1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^11], AppendTo[a, n]], {n, 1, 1400}]; a

is(n)=isprime(1+n^2+n^4+n^6+n^8+n^10+n^11) \\ Charles R Greathouse IV, Jun 13 2017

cp's OEIS Frontend

A124176 Consider the map f that sends m to m + (sum of odd digits of m) - (sum of even digits of m). Sequence gives numbers m such that f^(k)(m) = m for some k.

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A126908 Numbers k such that 1 + k^2 + k^4 + k^6 + k^7 is prime.

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A126916 Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23 is prime.

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A304439 Add to n the sum of its odd digits minus the sum of its even digits.

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A304440 Add to n the sum of its even digits minus the sum of its odd digits.

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A076164 Numbers n such that sum of squares of even digits of n equals sum of squares of odd digits of n.

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A126906 Smallest k such that 1 + k^(2*n+1) + Sum_{j=1..n} k^(2*j) is prime.

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A126907 Numbers n such that 1 + n^2 + n^4 + n^5 is prime.

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A126906 Smallest k such that 1 + k^(2n+1) + Sum_{j=1..n} k^(2j) is prime.