A236225
Sum of the seventeenth powers of the first n primes.
Original entry on oeis.org
131072, 129271235, 763068724360, 233393582711567, 505680422082005338, 9156096341463343271, 836396358227800107448, 6316783216012602293387, 147366822776675571219490, 7404514559506748686057599, 29954631333669491864740510, 486442572159704647268887427
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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Table[Sum[Prime[k]^17, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^17] (* Harvey P. Dale, Nov 05 2016 *)
A236226
Sum of the eighteenth powers of the first n primes.
Original entry on oeis.org
262144, 387682633, 3815084948258, 1632228682858707, 5561549542175090188, 118016956494132483317, 14181101408561857474326, 118308451706473099007167, 3362459361601721384307536, 213819743726773841714612697, 912873363725818880253782938
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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Table[Sum[Prime[k]^18, {k, n}], {n, 1000}]
Accumulate[Prime[Range[20]]^18] (* Harvey P. Dale, Jul 08 2024 *)
A236227
Sum of the nineteenth powers of the first n primes.
Original entry on oeis.org
524288, 1162785755, 19074649113880, 11417969834487023, 61170508418249033314, 1523090798793695143991, 240595526483945019991144, 2219015182144258609115123, 76834486109734969171023610, 6180095732699726458749873279, 27850757952670122653464150750
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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Table[Sum[Prime[k]^19, {k, n}], {n, 1000}]
A232770
Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer.
Original entry on oeis.org
2, 83, 1979, 2081, 2326469, 6356923, 7170679, 63812027, 4652001719, 241949473277, 163220642765623, 1260677492111911, 8150959175977039
Offset: 1
a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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t = {}; sm = 0; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^13); s==0 \\ Charles R Greathouse IV, Nov 30 2013
A232848
Prime(k), where k divides Sum_{i=1..k} prime(i)^15.
Original entry on oeis.org
2, 59, 97, 127, 12517, 54581, 83921, 89273, 1396411, 2562719, 4952183, 29201281, 35562101, 47567557, 111213143, 184201627, 1172476337, 7309217299, 287609314877, 5173838081669, 408907258717171, 1357729730868191, 66413899001789557
Offset: 1
a(2) = 59, because 59 is the 17th prime and the sum of the first 17 primes^15 = 455708280934100194626604550 when divided by 17 equals 26806369466711776154506150 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n),
A131275.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^15; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^15); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^15)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A232963
Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.
Original entry on oeis.org
2, 1933, 3217, 41681, 114311, 2743691233, 7252463461, 28682755720447, 2839633449523319
Offset: 1
a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^14; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^14)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233192
Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.
Original entry on oeis.org
2, 97, 277, 23311, 61583, 6133811, 210952097, 359643241, 5451597181, 42641466149, 51575229001, 199655689679, 248181386429, 61646670874849, 82153230089767, 212374157550341, 11432141933990629, 15031011453909223
Offset: 1
a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^11 = 12718098700540100969050 when divided by 25 equals 508723948021604038762 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^11; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^11); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^11)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233460
Prime(n), where n is such that (sum_{i=1..n} prime(i)^16) / n is an integer.
Original entry on oeis.org
2, 28751, 62639, 4620757, 6478193, 2298168044423, 128195718927553
Offset: 1
a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^16 = 65536 when divided by 1 equals 65536 which is an integer.
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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t = {}; sm = 0; Do[sm = sm + Prime[n]^16; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^16); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^16)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233555
Prime(m), where m is such that (Sum_{i=1..m} prime(i)^17) / m is an integer.
Original entry on oeis.org
2, 5724469, 10534369, 16784723, 33330911, 189781037, 8418091991, 58605633953, 109388266843, 448366797199, 1056238372873, 24603683667221, 86982253895059, 100316149840769, 164029709175817, 542295448805641, 685217940914237, 1701962315686097, 23064173255594491
Offset: 1
a(1) = 2, because 2 is the 1st prime and the sum of the first 1 primes^17 = 131072 when divided by 1 equals 131072 which is an integer.
Cf.
A085450 (smallest m > 1 that divide Sum_{k=1..m} prime(k)^n).
-
t = {}; sm = 0; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^17); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^17)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013
A233575
Prime(m), where m is such that (Sum_{i=1..m} prime(i)^18) / m is an integer.
Original entry on oeis.org
2, 157, 1697, 190573, 167719729, 22092660553, 57613776809, 4386989244577, 91982826261331, 13432259712845291
Offset: 1
a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^18 = 7222759943091280921446062146835136523956 when divided by 37 equals 195209728191656241120163841806355041188 which is an integer.
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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t = {}; sm = 0; Do[sm = sm + Prime[n]^18; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
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is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^18); s==0 \\ Charles R Greathouse IV, Nov 30 2013
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S=n=0;forprime(p=1,,(S+=p^18)%n++||print1(p",")) \\ - M. F. Hasler, Dec 01 2013
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