A261338 Primes p such that digitsum(p) > digitsum(q) where q is the next prime after p.

7, 19, 29, 37, 47, 59, 67, 79, 89, 97, 109, 127, 149, 157, 167, 179, 199, 229, 239, 257, 269, 277, 293, 307, 317, 349, 359, 367, 379, 389, 397, 419, 439, 449, 457, 479, 487, 499, 509, 557, 569, 587, 599, 607, 619, 647, 659, 677, 683, 691, 719, 727, 739, 743, 757

Offset

1,1

Comments

A000040(n) for n such that A007605(n) > A007605(n+1). - Robert Israel, Aug 17 2015

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

19 is in the sequence because it is prime; [digitsum(19) = 1 + 9 = 10] > [digitsum(23) = 2 + 3 = 5] where 19 and 23 are consecutive primes.
47 is in the sequence because it is prime; [digitsum(47) = 4 + 7 = 11] > [digitsum(53) = 5 + 3 = 8] where 47 and 53 are consecutive primes.

Maple

with(numtheory): A261338:= proc() local k, k1, p; p:=ithprime(n); k:=(add(d, d=convert(p, base, 10))); k1:=(add(d, d=convert(nextprime(p), base, 10))); if k > k1 then RETURN (p); fi; end: seq(A261338 (), n=1..300);

Mathematica

A261338 = {}; Do[p = Prime[n]; k = Plus @@ IntegerDigits[p]; k1 = Plus @@ IntegerDigits[NextPrime[p]]; If[k > k1, AppendTo[A261338, p]], {n, 1, 300}]; A261338 (* Bajpai *)
Prime[Select[Range[100], (Plus@@IntegerDigits[Prime[#]]) >
(Plus@@IntegerDigits[Prime[# + 1]]) &] (* Alonso del Arte, Aug 16 2015 *)
Prime[#]&/@SequencePosition[Table[Total[IntegerDigits[p]], {p, Prime[Range[ 150]]}], _?(#[[1]]>#[[2]]&)][[All, 1]]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 10 2020 *)

Prog

(PARI) forprime(p = 1, 300, q=nextprime(p+1); if(sumdigits(p) > sumdigits(q), print1(p, ", ")));
(Magma) [NthPrime(n) : n in [1..200]  |  &+Intseq(NthPrime(n)) ge &+Intseq(NthPrime(n+1))];

Crossrefs

Cf. A000040, A007605.

Sequence in context: A175366 A117609 A122072 * A352338 A109355 A272404

Adjacent sequences: A261335 A261336 A261337 * A261339 A261340 A261341

Keyword

nonn,base

Author

K. D. Bajpai, Aug 15 2015

Status

approved