Vicente Izquierdo Gomez has authored 7 sequences.
A257974
Prime numbers that are not the sum of one or more consecutive triangular numbers.
Original entry on oeis.org
2, 5, 7, 11, 13, 17, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283
Offset: 1
From _Michael De Vlieger_, Nov 06 2015: (Start)
3 is a triangular number thus is not a term.
The triangular numbers <= 7 are {1, 3, 6}. None of these are 7. 7 is not found among the sums of adjacent pairs of terms, i.e., {{1, 3}, {3, 6}} = {4, 9}. The sum of all numbers {1, 3, 6} = 10. Thus 7 is a term.
The triangular numbers <= 19 are {1, 3, 6, 10, 15}. 19 is not a triangular number. 19 is not found among sums of pairs of adjacent terms {4, 9, 16, 25} nor among those of quartets of adjacent terms {20, 34}, but is found among sums of triples of adjacent terms {10, 19, 31}. Thus 19 is not a term. (End)
-
isA257974 := proc(n)
if isprime(n) then
return not isA034706(n) ;
else
false ;
end if;
end proc:
for n from 0 to 400 do
if isA257974(n) then
printf("%d,",n) ;
end if;
end do: # R. J. Mathar, Dec 14 2015
-
t = Array[Binomial[# + 1, 2] &, {10^4}]; fQ[n_] := Block[{s}, s = TakeWhile[t, # <= n &]; AnyTrue[Flatten[Total /@ Partition[s, #, 1] & /@ Range[Length@ s - 1]], # == n &]]; Select[Prime@ Range@ 120, ! fQ@ # &] (* Michael De Vlieger, Nov 06 2015, Version 10 *)
A259744
Smallest prime p such that, for every positive integer k <= n, the concatenation of p, prime(k)^2 and reverse(p) is prime.
Original entry on oeis.org
11, 17, 1097, 7949, 780587, 123638027, 3259714649, 76526081651
Offset: 1
a(3)=1097 because 109747901 (1097&2^2&7901) and 109797901 (1097&3^2&7901) and 1097257901 (1097&5^2&7901) are prime numbers, and 1097 is the smallest prime for which this is the case.
-
f[n_, k_] := FromDigits[Join[
IntegerDigits[n], IntegerDigits[Prime[k]^2],
Reverse[IntegerDigits[n]]]]
a[n_] := Module[{p = 2, k = 1},
While[k <= n,
If[PrimeQ[f[p, k]], k++, p = NextPrime[p]; k = 1];
];
Return[p]
](* Kellen Myers, Aug 16 2015 , note this is very slow *)
A234540
Nonprimes k that divide the sum of the nonprimes up to k.
Original entry on oeis.org
1, 22, 25, 118, 414, 2745, 10623, 63201, 1039161, 1693864, 2285297, 52962021, 66998865, 232974402, 315796805, 336125877, 834972771, 1233903294, 1309750075, 1617454215, 2056836133, 5455816485, 8589896196, 9030058217, 10622144467, 12324258770, 33725308558
Offset: 1
a(2) = 22 because 1 + 4 + 6 + 8 + 9 + 10 + ... + 22 = 176 and 176/22 = 8.
-
s = 0; Do[If[PrimeQ[k], Continue[]]; s += k; If[Mod[s, k] == 0, Print[k]], {k, 10^10}] (* Gomez *)
Select[Range[10^4], Not[PrimeQ[#]] && Divisible[Sum[Boole[Not[PrimeQ[m]]]m, {m, #}], #] &] (* Alonso del Arte, Dec 29 2013 *)
-
v=List([s=1]); forcomposite(n=4,1e9,if(s%n==0, listput(v,n)); s+=n); Vec(v) \\ Charles R Greathouse IV, Dec 29 2013
A216638
First appearance of the Fibonacci numbers in the decimals of Pi.
Original entry on oeis.org
1, 1, 6, 9, 4, 11, 110, 93, 86, 130, 11, 1638, 229, 3056, 268, 1510, 10118, 11477, 727, 17711, 83295, 59861, 22334, 19659, 301848, 977089, 59943, 414086, 536681, 649382, 2729036, 68232754, 17793212, 33986473, 695781, 135830965, 117951651, 36978613, 170243036, 366567058
Offset: 1
Fibonacci(4) is 3, 3 appears for the first time in decimals of Pi in position 9, so a(4) = 9.
-
(* Determine the decimal digits of Pi following the decimal point. *)
decimalPiDigits[n_] := First@RealDigits[Pi, 10, n, -1];
(* Find the position of first occurrence of 'sublist' in 'list', or Indeterminate if it doesn't occur. *)
firstPosition[sublist_, list_] :=
With[{p = SequencePosition[list, sublist]},
If[Length[p] == 0, Indeterminate, First@First@p]];
(* Find the first occurrence of the given digits in the decimal digits of Pi by calculating ever more digits of Pi, as needed. *)
findDigitSequenceInDecimalPiDigits[seq_] :=
First@NestWhile[
With[
{
numdigits = Max[1, 2*Last[#]] (*
How many digits will we calculate in this iteration? *)
},
{firstPosition[seq, decimalPiDigits[numdigits]], numdigits}
] &,
{Indeterminate, 0},
Not@*IntegerQ@*First
];
(* Find the first 30 entries. *)
Table[findDigitSequenceInDecimalPiDigits[
IntegerDigits@Fibonacci[n]], {n, 1, 30}]
(* Sidney Cadot, Feb 25 2023 *)
A216133
In the decimal expansion of Pi, the first occurrence of these primes begins at a prime position.
Original entry on oeis.org
7, 19, 31, 41, 43, 79, 89, 107, 137, 157, 197, 233, 263, 271, 293, 317, 367, 379, 433, 449, 479, 491, 499, 601, 641, 653, 673, 751, 757, 761, 769, 787, 797, 821, 823, 827, 853, 887
Offset: 1
The first 19 in the decimal expansion of Pi (see A000796) starts in position 37, which is a prime.
-
pos_in_Pi={1,6,9,2,4,7,13,11,5,49,94,148,110,1,3,....};
s={};Do[If[PrimeQ[x]&&PrimeQ[pos_in_Pi[[x]]],AppendTo[s,pos_in_Pi]],{x,Length[v]}];s
A215533
Numbers n such that n^s(n) + 1 is a prime, where s(n) is the sum of the digits of n.
Original entry on oeis.org
1, 2, 4, 10, 20, 100, 110, 152, 220, 242, 736, 790, 800, 916, 1010, 1078, 1106, 1232, 1528, 1636, 1834, 2284, 2330, 2392, 2600, 3100, 3562, 3904, 4000, 4066, 4228, 4444, 4552, 5056, 6082, 6208, 6226, 7810, 8170, 8530, 9520
Offset: 1
-
t = {}; Do[If[PrimeQ[(n^Total[IntegerDigits[n]]) + 1], AppendTo[t, n]], {n, 10000}]; t
Select[Range[10000],PrimeQ[#^Total[IntegerDigits[#]]+1]&] (* Harvey P. Dale, Aug 26 2019 *)
A214629
Primes p such that the sum of the digits plus the product of the digits is a prime.
Original entry on oeis.org
11, 13, 19, 23, 29, 31, 37, 43, 53, 59, 61, 73, 79, 89, 97, 101, 223, 263, 283, 401, 409, 443, 601, 607, 809, 823, 829, 883, 1013, 1019, 1031, 1033, 1039, 1051, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1163, 1171, 1181, 1187, 1193, 1213, 1231, 1259
Offset: 1
11 is in the sequence because A061762(11) = 3 is prime.
-
f:= proc(n) local L;
L:= convert(n,base,10);
convert(L,`+`)+convert(L,`*`)
end proc:
select(p -> isprime(f(p)), [seq(ithprime(i),i=1..1000)]); # Robert Israel, May 07 2021
-
f[n_] := Module[{in = IntegerDigits[n]}, Times @@ in + Plus @@ in];Select[Prime[Range[300]], PrimeQ[f[#]] &]
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