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 1-4 of 4 results.

A307008 Numbers that are both prime-indexed primes and lucky-indexed lucky numbers.

Original entry on oeis.org

31, 367, 991, 1087, 1471, 3259, 3559, 5851, 6661, 6841, 8719, 9661, 10723, 11953, 13513, 18181, 20341, 21529, 22651, 23563, 25057, 31189, 39451, 70207, 72727, 75937, 81931, 85843, 87931, 92569, 93169, 108643, 131071, 136483, 143797, 149503, 150991, 163309
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2019

Keywords

Comments

Intersection of A006450 and A032639.

Crossrefs

Cf. A006450, A031157, A032639, A057698, A307009, A307010.

Programs

  • Mathematica
    m = 10^4; L = Table[2*i + 1, {i, 0, m}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; ll = L[[Select[L, # <= Length[L] &]]]; pp = Prime@ Prime@ Range@ PrimePi@ PrimePi@ (2m); Intersection[pp,ll] (* after Jean-François Alcover at A000959 and Giovanni Resta at A303403 *)

A307010 Numbers that are prime-indexed primes, lucky-indexed lucky numbers, lucky-indexed primes and prime-indexed lucky numbers.

Original entry on oeis.org

367, 687331, 1983913, 2278033, 2400793, 2760361, 3531247, 5840767, 9429223, 11894593, 13201483, 13371751, 13597357, 13755361, 19782127, 24772663, 25607341, 34723783, 51279127, 56208967, 59215327, 71039257, 74498731, 83170537, 97983187, 109510909, 124762969
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2019

Keywords

Comments

Intersection of A006450, A032639, A032605 and A032606.
Intersection of A307008 and A307009.

Crossrefs

Cf. A006450, A031157, A032605, A032606, A032639, A307008, A307009.

Programs

  • Mathematica
    m = 10^4; L = Table[2*i + 1, {i, 0, m}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; P = Select[ Range[2m], PrimeQ]; lp = L[[Select[P, # <= Length[L] &]]]; pl = P[[Select[L, # <= Length[P] &]]]; pp = P[[Select[P, # <= Length[P] &]]]; ll = L[[Select[L, # <= Length[L] &]]]; Intersection[lp, pl, pp, ll] (* after Jean-François Alcover at A000959 *)

A318487 Even numbers that are not the sum of two lucky-indexed lucky numbers.

Original entry on oeis.org

4, 6, 10, 12, 16, 18, 20, 24, 26, 30, 34, 36, 40, 44, 46, 48, 54, 58, 60, 66, 68, 72, 74, 76, 78, 82, 86, 90, 92, 96, 100, 102, 104, 106, 110, 114, 116, 120, 122, 124, 128, 130, 134, 138, 140, 144, 146, 152, 154, 156, 158, 164, 168, 170, 176, 178, 182, 184
Offset: 1

Views

Author

Amiram Eldar, Aug 27 2018

Keywords

Comments

Conjecture (checked up to 10^7): every even number larger than 199254 is the sum of two lucky-indexed lucky numbers, so this sequence is finite with 1714 terms.

Examples

			28 is not in this sequence since 28 = 7 + 21 and 7 and 21 are lucky-indexed lucky numbers (A032639).

Links

Crossrefs

Cf. A000959, A032639, A303403.

Programs

  • Mathematica
    L = Table[2*i + 1, {i, 0, 150000}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; a = L[[Select[L, # <= Length[L] &]]]; v = Select[Range[2, 300000, 2], IntegerPartitions[#, {2}, a] == {} &]; (* after Jean-François Alcover at A000959 and Giovanni Resta at A303403 *)

A319824 Numbers that are not the sum of distinct lucky-indexed lucky numbers.

Original entry on oeis.org

2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 30, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 54, 55, 58, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 79, 82, 83, 86, 89, 90, 93, 96, 97, 98, 99, 100, 103
Offset: 1

Views

Author

Amiram Eldar, Sep 28 2018

Keywords

Comments

Analogous to A213356 with primes instead of lucky numbers.
Conjecture: this sequence is finite with the last term being a(98) = 373.

Links

Crossrefs

Cf. A000959, A032639, A213356, A318487.

Programs

  • Mathematica
    L = Table[2*i + 1, {i, 0, 2500}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; a = L[[Select[L, # <= Length[L] &]]]; nn=Length[a]; t=Rest[CoefficientList[Series[Product[(1+x^(a [[k]])), {k, nn}], {x, 0, nn*nn}], x]]; Flatten[Position[t, 0]] (* after Jean-François Alcover at A000959 *)
Showing 1-4 of 4 results.

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