A303403 -id:A303403 - cp's OEIS frontend

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

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

Amiram Eldar, Mar 19 2019

nonn

Intersection of A006450 and A032639.

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

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 *)

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

Amiram Eldar, Aug 27 2018

nonn

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.

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

Amiram Eldar, Table of n, a(n) for n = 1..1714

Cf. A000959, A032639, A303403.

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 *)

cp's OEIS Frontend

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

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